1. Nikita bought 30 kg of wheat at the rate of Rs. 9.50 per kg and 40 kg of wheat at the rate of Rs. 8.50 per kg and mixed them. She sold the mixture at the rate of Rs. 8.90 per kg. Her total profit or loss in the transaction was
a) Rs. 2 loss
b) Rs. 2 profit
c) Rs. 7 loss
d) Rs.7 profit
Explanation C.P. of 70 kg wheat
= Rs. (30 × 9.50 + 40 × 8.50)
= Rs. (285 + 340)
= Rs. 625
S.P. of 70 kg wheat
= Rs. (70 × 8.90)
= Rs. 623
∴ Loss = Rs. (625 - 623) = Rs. 2
2. An article is sold at a gain of 15% . Had it been sold for Rs. 27 more, the profit would have been 20% . The cost price of the article is = ?
a) Rs. 500
b) Rs. 700
c) Rs. 540
d) Rs. 545
Explanation:
$$\eqalign{ & {\text{Let cost}}\,{\text{price}}\,{\text{be}}\,x \cr & {\text{profit}} = \frac{{15x}}{{100}} \cr & {\text{If}}\,{\text{it}}\,{\text{was}}\,{\text{sold}}\,{\text{for}}\,{\text{Rs}}{\text{.}}\,27\,{\text{more,}} \cr & {\text{profit}} = \frac{{20x}}{{100}} \cr & \frac{{20x}}{{100}} - \frac{{15x}}{{100}} = 27 \cr & \frac{{5x}}{{100}} = 27 \cr & \frac{x}{{20}} = 27 \cr & \therefore x = 540 \cr} $$
3. A businessman bought an article and sold it at a loss of 5% . If he had bought it for 10% less and sold it for Rs. 33 more, he would have had a profit of 30% . The cost price of the article is = ?
a) Rs. 330
b) Rs. 155
c) Rs. 150
d) Rs. 300
Explanation: Let the CP1 of article = 100x
Initial SP1 = 100x - 5% of 100x = 100x - 5x = 95x
Now, If He brought article at 10% discount. Therefore CP2 = 90x
Now SP2 = 90x + 30% of 90x = 90x + 27x =117x
According to question
SP2 - SP1 = 33
⇒ 117x - 95x = 33
⇒ 22x = 33
⇒ x = $$\frac{33}{22}$$
⇒ x = $$\frac{3}{2}$$
Initial Cost of article
= 100 × $$\frac{3}{2}$$
= Rs. 150
4. A profit of 12% is made when a mobile phone is sold at Rs. P and there is 4% loss when the phone is sold at Rs. Q. Then Q : P is = ?
a) 1 : 1
b) 6 : 7
c) 4 : 5
d) 3 : 1
Explanation:
$$\eqalign{ & {\text{CP}} = {\text{P}} \times \frac{{100}}{{112}} \cr & {\text{CP}} = {\text{Q}} \times \frac{{100}}{{96}} \cr & \frac{{{\text{P}} \times 100}}{{112}} = \frac{{{\text{Q}} \times 100}}{{96}} \cr & {\text{P}}:{\text{Q}} = 112:96 \cr & {\text{P}}:{\text{Q}} = 56:48 \cr & {\text{P}}:{\text{Q}} = 7:6 \cr & {\text{Q}}:{\text{P}} = 6:7 \cr} $$
5. Manish purchased 25 kg of rice @ Rs. 32 per kg and 15 kg of rice @ Rs. 36 per kg. He mixed the two varieties of rice and sold it @ Rs. 40.20 per kg. What is the percent profit earned ?
a) 20%
b) 25%
c) 30%
d) 40%
Explanation:
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{. of 40 kg rice}} \cr & = {\text{Rs}}.\left( {25 \times 32 + 15 \times 36} \right) \cr & = {\text{Rs}}.\left( {800 + 540} \right) \cr & = {\text{Rs}}.1340. \cr & {\text{S}}{\text{.P}}{\text{. of 40 kg rice}} \cr & = {\text{Rs}}.\left( {40 \times 40.20} \right) \cr & = {\text{Rs}}{\text{. }}1608. \cr & {\text{Profit}} = {\text{Rs}}.\left( {1608 - 1340} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}268. \cr & \therefore {\text{Profit }}\% = \left( {\frac{{268}}{{1340}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 20\% \cr} $$
6. By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg, a shopkeeper makes a profit of 18% . If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does he other brand cost ?
a) Rs. 110
b) Rs. 120
c) Rs. 140
d) None of these
Explanation: Let the cost of the other brand be Rs. x per kg.
C.P. of 5 kg = Rs. (2 × 200 + 3 × x) = Rs. (400 + 3x)
S.P. of 5 kg = Rs. (5 × 177) = Rs. 885
$$\eqalign{ & \therefore \frac{{885 - \left( {400 + 3x} \right)}}{{400 + 3x}} \times 100 = 18 \cr & \Leftrightarrow \frac{{485 - 3x}}{{400 + 3x}} = \frac{9}{{50}} \cr & \Leftrightarrow 24250 - 150x = 3600 + 27x \cr & \Leftrightarrow 177x = 20650 \cr & \Leftrightarrow x = \left( {\frac{{350}}{3}} \right) = 116\frac{2}{3} \cr & {\text{So, cost of the other brand}} \cr & = {\text{Rs}}{\text{. }}116.66 \cr} $$
7. A milkman cheats his customer in two ways. He mixes 10% water in pure milk and increases the price of milk by 10% . He purchases 20 kg pure milk at a rate of Rs. 15 per kg. His total profit by selling it is
a) Rs. 40
b) Rs. 63
c) Rs. 80
d) Rs. 100
Explanation: C.P. of 20 kg milk = Rs. (20 × 15) = Rs. 300
Quantity of water added = 10% of 20 kg = 2 kg
S.P. of 1 kg mixture = 110% of Rs. 15 = Rs. 16.50
S.P. of 22 kg mixture = Rs. (22 × 16.50) = Rs. 363
Profit = Rs. (363 - 300) = Rs. 63
8. A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is = ?
a) 99 : 125
b) 25 : 37
c) 50 : 61
d) 45 : 56
Explanation:According to the question,
| Cost Price | : | Marked Price |
| (100 - Discount) | : | (100 + Profit) |
| 100 - 10 | : | 100 + 12 |
| 90 | : | 112 |
| 45 | : | 56 Answer |
9. A tradesman allows a discount of 15% on the marked price. How much above the cost price must he mark his goods as to gain 19% ?
a) 34%
b) 40%
c) 25%
d) 30%
Explanation: According to the question,
| Cost Price | : | Marked Price |
| (100 - Discount) | : | (100 + Profit) |
| 100 - 15 | : | 100 + 19 |
| 85 | : | 119 |
| 34 units more | ||
$$\eqalign{ & {\text{Raised}}\% = \frac{{34}}{{85}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 40\% \cr} $$
10. A shopkeeper allows 23% commission on his advertised price and still makes a profit of 10% . If he gains Rs. 56 on one item, his advertised price of the item, in Rs. is = ?
a) 820
b) 780
c) 790
d) 800
Explanation: Advertised price of the item = N
∴ Commission on advertised price of the article = $$\frac{{N \times 23}}{{100}}$$
Price after commission = $$N - \frac{{23N}}{{100}} = \frac{{77N}}{{100}}$$
$$\eqalign{ & \therefore {\text{CP}}\,{\text{of}}\,{\text{the}}\,{\text{item}} \cr & \frac{{\frac{{77N}}{{100}} \times 100}}{{100 + 10}} \cr & = \frac{{77N}}{{110}} \cr & = \frac{{7N}}{{10}} \cr & {\text{Profit}} = \frac{{77N}}{{110}} - \frac{{7N}}{{10}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{7N}}{{110}} \cr & \Rightarrow 56 = \frac{{7N}}{{110}} \cr & \therefore N = \frac{{56 \times 100}}{7} = 800 \cr} $$
11. When a plot is sold for Rs. 18700, the owner loses 15% . At what price must the plot be sold in order to gain 15% ?
a) Rs. 21,000
b) Rs. 22,500
c) Rs. 25,300
d) Rs. 25,800
Explanation Let the new S.P. be Rs. x
Then, 85 : 18700 = 115 : x
$$\eqalign{ & \Rightarrow x = \left( {\frac{{18700 \times 115}}{{85}}} \right) \cr & \Rightarrow x = 25300 \cr} $$
12. A book seller sells a book at a profit of 10% . If he had bought it at 4% less and sold it for Rs. 6 more. He would have gained $$18\frac{3}{4}$$% . The cost price of the book is = ?
a) Rs. 130
b) Rs. 140
c) Rs. 150
d) Rs. 160
Explanation: Let the CP of the book = x
Gain = 10%
SP = $$\frac{{110{\text{x}}}}{{100}}$$
If he had bought it at 4% less and sold it for Rs 6 more,
$$\eqalign{ & {\text{CP}} = \frac{{96x}}{{100}} \cr & {\text{SP}} = \frac{{110x}}{{100}} + 6 \cr & {\text{Gain}} = \left( {\frac{{110x}}{{100}} + 6} \right) - \frac{{96x}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{{14x}}{{100}}} \right) + 6 \cr} $$
Now, the gain =$$18\frac{3}{4}\% = \frac{{75}}{4}\% $$
Therefore,
$$\eqalign{ & \Rightarrow \frac{{14x}}{{100}} + 6 = \frac{{96x}}{{100}} \times \frac{{75}}{{400}} \cr & \Rightarrow \frac{{14x}}{{100}} + 6 = \frac{{96x}}{4} \times \frac{3}{{400}} \cr & \Rightarrow 14x + 600 = \frac{{96x}}{4} \times \frac{3}{4} \cr & \Rightarrow 14x + 600 = 6x \times 3 \cr & \Rightarrow 14x + 600 = 18x \cr & \Rightarrow 18x - 14x = 600 \cr & \Rightarrow 4x = 600 \cr & \therefore x = 150 \cr} $$
13. A businessman sells a commodity at 10% profit. If he had bought it at 10% less and sold it for Rs. 2 less, then he would have gained $$16\frac{2}{3}$$% . The cost price of the commodity is = ?
a) Rs. 32
b) Rs. 36
c) Rs. 40
d) Rs. 48
Explanation: Let the CP1 of commodity = 100x
Initial SP1 = 100x + 10% of 100x = 100x + 10x = 110x
Now, If He brought table at 10% discount. Therefore CP2 = 90x
Now SP2 = 90x + $$16\frac{2}{3}$$% of 90x = 90x + 15x =105x
According to question
SP1 - SP2 = 2
⇒ 110x - 105x = 2
⇒ 5x = 2
⇒ x = $$\frac{2}{5}$$
Initial Cost of commodity = 100 × $$\frac{2}{5}$$ = Rs. 40
14. A fruit seller sells mangoes at the rate of Rs. 9 per kg and thereby loses 20% . At what price per kg, he should have sold, them to make a profit of 5% ?
a) Rs. 11.81
b) Rs. 12
c) Rs. 12.25
d) Rs. 12.31
Explanation: Let the new S.P. be Rs. x
$$\eqalign{ & {\text{Then,}} \cr & 80:9 = 105:x \cr & \Rightarrow x = \left( {\frac{{9 \times 105}}{{80}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 11.81 \cr} $$
15.Raju purchased an item for Rs. 8200 and sold it at a gain of 25% . From that amount he purchased another item and sold it at a loss of 20% . What is his overall gain loss ?
a) Loss of Rs. 120
b) Gain of Rs. 120
c) Loss of Rs. 140
d) Neither loss nor gain
Explanation:
$$\eqalign{ & {\text{Initial investment}} \cr & = {\text{Rs}}.8200 \cr & {\text{S}}{\text{.P}}{\text{.of }}{{\text{1}}^{{\text{st}}}}{\text{ term}} \cr & = {\text{Rs}}.\left( {\frac{{125}}{{100}} \times 8200} \right) \cr & = {\text{Rs}}{\text{. }}10250 \cr & {\text{C}}{\text{.P}}{\text{.of }}{{\text{2}}^{{\text{nd}}}}{\text{ term}} \cr & = {\text{Rs}}{\text{. }}10250 \cr & {\text{loss}} = 20\% \cr & {\text{Final receipt}} \cr & = {\text{S}}{\text{.P}}{\text{.of }}{{\text{2}}^{{\text{nd}}}}{\text{ term}} \cr & = {\text{Rs}}.\left( {\frac{{80}}{{100}} \times 10250} \right) \cr & = {\text{Rs}}{\text{. }}8200 \cr} $$
Since initial investment = final receipt, there was neither gain nor loss
16. Left pan of a faculty balance weighs 100 grams more than its right pan. A shopkeeper keeps the weight measure in the left pan while buying goods but keeps it in the right pan while selling his goods. He uses only 1 kg weight measure. If he sells his goods at the listed cost price, what is his gain ?
a) $$\frac{{100}}{{11}}$$%
b) $$\frac{{200}}{{11}}$$%
c) $$\frac{{100}}{{9}}$$%
d) $$\frac{{200}}{{9}}$$%
Explanation: Let the C.P. of 1 kg goods be Rs. 1
Then,
He buys 1100 g goods for Rs. 1 and sells 900 g goods for Rs. 1
∴ C.P. of 1100 g goods = Rs. 1
⇒ C.P. of 900 g goods
$$\eqalign{ & = {\text{Rs}}.\left( {\frac{1}{{1100}} \times 900} \right) \cr & = {\text{Rs}}.\frac{9}{{11}} \cr} $$
S.P. of 900 g goods = Rs. 1
$$\eqalign{ & {\text{Gain = Rs}}.\left( {1 - \frac{9}{{11}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\frac{2}{{11}} \cr & \therefore {\text{Gain }}\% \cr & = \left( {\frac{2}{{11}} \times \frac{{11}}{9} \times 100} \right)\% \cr & = \frac{{200}}{9}\% \cr} $$
17. A dishonest dealer sells the goods at 20% loss on cost price but uses 15% less weight. What is his percentage profit or loss ?
a) $$5\frac{{11}}{{17}}$$ % loss
b) $$5\frac{{15}}{{17}}$$ % loss
c) $$5\frac{{15}}{{17}}$$ % gain
d) $$5\frac{{11}}{{17}}$$ % gain
Explanation:
$$\eqalign{ & {\text{Gain/loss }}\% \cr & = \left\{ {\left( {\frac{{y - x}}{{100 - y}}} \right) \times 100} \right\}\% \cr & = \left\{ {\left( {\frac{{15 - 20}}{{100 - 15}}} \right) \times 100} \right\}\% \cr & = \left( {\frac{{ - 5}}{{85}} \times 100} \right)\% \cr & = - \frac{{100}}{{17}}\% \cr & = - 5\frac{{15}}{{17}}\% \cr} $$
Since it is -ve, hence it is a loss.
18. While selling to the retailer, a company allows 30% discount on the marked price of their products. If the retailer sells those products at marked price, his profit % will be = ?
a) 30%
b) $$\frac{{17}}{2}$$%
c) 40%
d) $$42\frac{6}{7}$$%
Explanation: Let the marked price = 100 units
According to the question,
\[{\text{100(MP)}}\xrightarrow{{30\% {\text{ discount}}}}{\text{70(SP)}}\] \[ \to \] CP of retailer
Cost price of retailer = 70
Retailer sold at Marked price = 100
Profit = Marked price - Cost price
= 100 - 70
= 30 units profit
$$\eqalign{ & \therefore {\text{Profit }}\% = \frac{{30}}{{70}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 42\frac{6}{7}\% \cr} $$
19. A trader marked the price of a commodity so as to include a profit of 25% , but allow discount of 16% on the marked price. His actual profit will be = ?
a) 16%
b) 25%
c) 5%
d) 9%
Explanation: Let CP be Rs. 100. Then, marked price = Rs. 125
$$\eqalign{ & {\text{SP}} = 84\% \,{\text{of}}\,{\text{Rs}}{\text{.}}\,125 \cr & \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,\left( {\frac{{84}}{{100}} \times 125} \right) \cr & \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,105 \cr} $$
∴ Profit = (105 - 100)% = 5%
20. A got 30% concession on the label price of an article and sold for Rs. 8750 with 25% profit on the price he bought. The label price was = ?
a) Rs. 13000
b) Rs. 16000
c) Rs. 12000
d) Rs. 10000
Explanation:
$$\eqalign{ & {\text{CP}} = {\text{Rs}}{\text{.}}\,\left( {\frac{{100}}{{125}} \times 8750} \right) \cr & \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,7000 \cr} $$
Let the labelled price be Rs. x
Then,
$$\eqalign{ & \frac{{70}}{{100}} \times x = 7000 \cr & \therefore x = {\text{Rs}}{\text{.}}\,\left( {\frac{{7000 \times 100}}{{70}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,10000 \cr} $$
21. A shopkeeper advertises for selling cloth at 4% loss. However, by using a false meter scale he actually gains 20% . What is the actual length of the scale ?
a) 70 cm
b) 75 cm
c) 80 cm
d) 90 cm
Explanation Let the percentage deduction in weight be y%
Then,
$$\eqalign{ & \frac{{y - 4}}{{100 - y}} \times 100 = 20 \cr & \Rightarrow \frac{{y - 4}}{{100 - y}} = \frac{1}{5} \cr & \Rightarrow 5y - 20 = 100 - y \cr & \Rightarrow 6y = 120 \cr & \Rightarrow y = 20 \cr} $$
Hence, for a meter, length used = (100 - 20)% of 1 m
= 80% of 100 cm = 80 cm
22. A trader professes to sell his goods at a nominal gain percentage but actually earns $$37\frac{1}{2}$$% profit by using false weight. If for a kg he uses a weight of 800 gm, what is the nominal gain percentage at which he claims to be selling his goods ?
a) 8%
b) 10%
c) 15%
d) 20%
Explanation: Let the required gain be x%
Percentage deduction in weight
$$\eqalign{ & = \left( {\frac{{200}}{{1000}} \times 100} \right)\% \cr & = 20\% \cr & \therefore \frac{{20 + x}}{{100 - 20}} \times 100 = 37\frac{1}{2} \cr & \Rightarrow \frac{{20 + x}}{{80}} = \frac{3}{8} \cr & \Rightarrow 20 + x = 30 \cr & \Rightarrow x = 10 \cr} $$
Hence, nominal gain percentage = 10%
23. A stockist wants to make some profit by selling sugar. He contemplates about various methods. Which of the following would maximize his profit ?
a) Sell sugar 10% profit
b) Use 900 g of weight instead of 1 kg
c) Mix 10% impurities in sugar and sell sugar at cost price
d) Increase the price by 5% and reduce the weight by 5%
Explanation: We find the net profit in each case :
1 → In this case, profit = 10%
$$\eqalign{ & 2 \to {\text{Profit}} = \left( {\frac{{100}}{{900}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 11\frac{1}{9}\% \cr} $$
3 → Let C.P. of sugar be Rs. 1 per kg
Then, he mixes 100 gm impurities and realizes the C.P. of 1.1 kg sugar by selling 1 kg of sugar.
S.P. of sugar = Rs. 1.10 per kg.
$$\eqalign{ & \therefore {\text{Profit}} = \left( {\frac{{0.1}}{1} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10\% \cr} $$
4 → Let C.P. of sugar be Rs. 1 per kg.
Since he weighs 950 gm instead of a kg, his actual
C.P. = Rs. 0.95
S.P. = 105% of Rs. 1 = Rs. 1.05
$$\eqalign{ & \therefore {\text{Profit}} = \left( {\frac{{0.10}}{{0.95}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10\frac{{10}}{{19}}\% \cr} $$
Clearly, the maximum profit is earned when he used a 900 gm weight for a kg.
24. A shopkeeper marks his goods 15% above the cost price, but allows 20% discount for cash. His net loss is = ?
a) 3%
b) 5%
c) 8%
d) 10%
Explanation: Let the cost price be Rs. 100
then the mark up price which is 15% above the cost price,
Mark price = (100 + 15% of 100) = Rs. 115
Shopkeeper gives a discount of 20% on mark up price, then the
Selling Price = (115 - 20% of 115) = Rs. 92
loss = 92 - 100 = Rs. -8
$$\eqalign{ & \% {\text{loss}} = \frac{{ - 8 \times 100}}{{100}} = - 8\% \cr & \therefore {\text{loss}} = 8\% \cr} $$
25. A trader allows a discount of 10% on the marked price. He still has a profit of 17% on the cost price. Find the profit percentage. If he sells at the marked price = ?
a) 27%
b) 33%
c) 30%
d) 19%
Explanation: Let the Marked price = Rs. 100
10% discount price will be = Rs. 90
$$17\% {\text{ of }}90 = \frac{{17 \times 100}}{{90}} \approx 20$$
∴ Cost price ≈ 90 - 20 ≈ 70
If the product is sell on marked price , then profit will be ≈ 30%
26.If the selling price of an article is doubled, then its loss profit percent is converted into equal profit percent. The loss percent on the article is = ?
a) $$26\frac{2}{3}$$ %
b) 33%
c) $$33\frac{1}{3}$$ %
d) 34%
Explanation: Let SP = Rs. x
According to question,
$$\eqalign{ & \left( {\frac{{CP - x}}{{CP}}} \right) \times 100 = \left( {\frac{{2x - CP}}{{CP}}} \right) \times 100 \cr & CP - x = 2x - CP \cr & 3x = 2CP \cr & x = \frac{2}{3}CP \cr & SP = \frac{2}{3}CP \cr & \frac{{SP}}{{CP}} = \frac{2}{3} > 1{\text{ unit loss}} \cr & {\text{Loss}}\% = \frac{1}{3} \times 100 = 33\frac{1}{3}\% \cr} $$
27. If an article sold at 200% profit then the ratio of its cost price to his selling price will be = ?
a) 1 : 2
b) 2 : 1
c) 1 : 3
d) 3 : 1
Explanation: Let the cost price of the article is = Rs. 100
According to the question,
\[{\text{100 (cp)}}\xrightarrow{{200\% {\text{ profit}}}}{\text{300 (sp)}}\]
\[{\text{Ratio of }}\frac{{{\text{CP}}}}{{{\text{SP}}}} = \frac{{100}}{{300}} = \frac{1}{3}\]
28.A fruit seller makes a profit of 20% by selling mangoes at a certain price. If he charges Rs. 1 more for each mango, he can make a profit of 40% . Find the selling price of a mango in the first case = ?
a) Rs.6
b) Rs.5
c) Rs. 5.50
d) Rs.7
Explanation:Let CP of 1 mango → 100
| CP | SP | ||
| 100 | → | 120 | [Profit→20] |
| 100 | → | 140 | [Profit→40] |
20 unit = Rs. 1
1 unit = $$\frac{1}{{20}}$$
120 unit = $$\frac{120}{{20}}$$ = Rs. 6
29. If selling price of an article is $$\frac{4}{3}$$ of its cost price, the profit in the transaction i
a) $$16\frac{2}{3}$$ %
b) $$20\frac{1}{2}$$ %
c) $$25\frac{1}{2}$$ %
d) $$33\frac{1}{3}$$ %
Explanation:
$$\eqalign{ & {\text{Let C}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. }}x. \cr & Then,S.P. = {\text{Rs}}.\frac{{4x}}{3} \cr & Gain = {\text{Rs}}.\left( {\frac{{4x}}{3} - x} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}\frac{x}{3} \cr & \therefore {\text{Gain }}\% \cr & = \left( {\frac{x}{3} \times \frac{1}{x} \times 100} \right)\% \cr & = 33\frac{1}{3}\% \cr} $$
30. If an article is sold for Rs. x, there is a loss of 15%. If the same article is sold for Rs. y, there is a profit of 15%. The ratio of left (y - x) to (y + x) is
a) 3 : 20
b) 20 : 3
c) 17 : 23
d) 20 : 23
Explanation:
$$\eqalign{ & {\text{Let C}}{\text{.P}}{\text{. of the article be Rs}}.p. \cr & Then, \cr & x = 85\% {\text{ of Rs}}{\text{. }}p = {\text{Rs}}.\frac{{85}}{{100}}p. \cr & {\text{and,}} \cr & y = 115\% {\text{ of Rs}}{\text{. }}p = {\text{Rs}}.\frac{{115}}{{100}}p. \cr & \therefore \left( {y - x} \right):\left( {y + x} \right) \cr & = \left( {\frac{{115}}{{100}}p - \frac{{85}}{{100}}p} \right):\left( {\frac{{115}}{{100}}p + \frac{{85}}{{100}}p} \right) \cr & = \frac{{30}}{{100}}p:\frac{{200}}{{100}}p \cr & = \frac{3}{{10}}:2 \cr & = 3:20 \cr} $$
31. Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of Rs. 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should he sell the mixture to make 30% profit ?
a) Rs. 14.80
b) Rs. 15.40
c) Rs. 15.60
d) Rs. 16.30
Explanation C.P. of 50 kg wheat
= Rs. (30 × 11.50 + 20 × 14.25)
= Rs. (345 + 285)
= Rs. 630
$$\eqalign{ & {\text{S}}{\text{.P}}{\text{. of 50 kg wheat}} \cr & = 130\% {\text{ of Rs}}{\text{.630}} \cr & = {\text{Rs}}.\left( {\frac{{130}}{{100}} \times 630} \right) \cr & = {\text{Rs}}.819 \cr & \therefore {\text{S}}{\text{.P}}{\text{. per kg}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{819}}{{50}}} \right) \cr & = {\text{Rs}}.16.38 \approx {\text{Rs}}.16.30 \cr} $$
32. A dealer buys dry fruit at the rate of Rs. 100, Rs. 80 and Rs. 60 per kg. He bought them in the ratio 12 : 15 : 20 by weight. He in total gets 20% profit by selling the first two and at last he finds he has no gain no loss in selling the whole quantity which he had. What was the percentage loss he suffered for the third quantity ?
a) 20%
b) 30%
c) 40%
d) 50%
Explanation: Suppose he bought 12 kg, 15 kg and 20 kg of the three varieties respectively.
Then,
Total C.P. = Rs. (12 × 100 + 15 × 80 + 20 × 60)
= Rs. (1200 + 1200 + 1200)
= Rs. 3600
Let the loss on the third quantity be x%
Than,
=120% of 2400 +(100 - x)% of 1200 = 3600
$$\eqalign{ & \Rightarrow \left( {\frac{6}{5} \times 24} \right) + \left( {\frac{{100 - x}}{{100}} \times 12} \right) = 36 \cr & \Rightarrow \frac{{100 - x}}{{100}} \times 12 = 36 - \frac{{144}}{5} = \frac{{36}}{5} \cr & \Rightarrow \frac{{100 - x}}{{100}} = \frac{{36}}{5} \times \frac{1}{{12}} = \frac{3}{5} \cr & \Rightarrow 500 - 5x = 300 \cr & \Rightarrow 5x = 200 \cr & \Rightarrow x = 40\% \cr} $$
33. A man purchased an article for Rs. 1500 and sold it at 25% above the cost price. If he has to pay Rs. 75 as tax on it his net profit percentage will be = ?
a) 25%
b) 30%
c) 15%
d) 20%
Explanation:
$$\eqalign{ & {\text{Cost price}} = {\text{Rs}}{\text{. 1500}} \cr & {\text{Profit after selling}} \cr & = 25\% {\text{ of }}1500 \cr & = {\text{Rs}}{\text{.375}} \cr & {\text{Net profit }} \cr & = {\text{Rs}}{\text{.375}} - {\text{Rs}}{\text{.75}} \cr & = {\text{Rs}}{\text{.300}} \cr & {\text{Net profit }}\% \cr & = \frac{{300}}{{1500}} \times 100 \cr & = 20\% \cr} $$
34. By selling some goods at Rs. 31, a salesman loses 7% on his output. Find the percentage profit of loss, when he sells the same at Rs. 35 = ?
a) Loss 7%
b) Profit 5%
c) Loss 5%
d) Profit 7%
Explanation: Selling price of goods = Rs. 31
Cost price of goods
$$\eqalign{ & = {\text{31}} \times \frac{{100}}{{93}} \cr & = {\text{Rs}}{\text{. }}\frac{{100}}{3} \cr & {\text{Profit }}\% \cr & = \frac{{35 - \frac{{100}}{3}}}{{\frac{{100}}{3}}} \times 100 \cr & = \frac{{\frac{5}{3}}}{{\frac{{100}}{3}}} \times 100 \cr & = 5\% \cr} $$
35.The marked price of an article is 10% higher than cost price. A discount of 10% is given on marked price. In this kind of seller bears = ?
a) No loss No gain
b) A loss of 5%
c) A gain of 1%
d) A loss of 1%
Explanation: Let cost price of the article is = Rs. 100
Marked price is 10% high of cost price mean = Rs. 110
Discount always given on marked price
10% discount of marked price means
$$ = \frac{{10}}{{100}} \times 110 = {\text{ Rs}}{\text{. 11}}$$
∴ Selling price = Marked price - Discount
Selling price = 110 - 11 = Rs. 99
$$\eqalign{ & \therefore {\text{Loss}}\% \cr & = \frac{{{\text{Cost price}} - {\text{Selling price}}}}{{{\text{Cost price}}}} \cr & \Rightarrow {\text{Loss}}\% = \frac{{100 - 99}}{{100}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{{100}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1\% \cr} $$
36. The profit earned after selling an article for Rs. 1754 is the same as loss incurred after selling the article for Rs. 1492. What is the cost price of the article?
a) Rs. 1523
b) Rs. 1589
c) Rs. 1623
d) Rs. 1689
Explanation: Let C.P. = Rs. x
Then, 1754 - x = x - 1492
⇒ 2x = 3246
⇒ x = 1623
37. Dinesh bought two radios for Rs. 1920. He sold one at a profit of 20% and other at a loss of $$6\frac{2}{3}$$% . If the selling price of both radios are same, then find the cost price of both radios = ?
a) Rs. 800 and Rs. 1120
b) Rs. 840 and Rs. 1080
c) Rs. 860 and Rs. 1060
d) Rs. 900 and Rs. 1020
Explanation: Let first radio CP is x second radio CP is 1920 - x
As is given,
$$x \times \frac{{\left( {100 + 20} \right)}}{{100}} = \left( {1920 - x} \right) \times $$ $$\frac{{\left( {100 - \frac{{20}}{3}} \right)}}{{100}}$$
$$\eqalign{ & 120 \times x = \left( {1920 - x} \right) \times \left( {\frac{{280}}{3}} \right) \cr & 360 \times x = \left( {1920 - x} \right) \times 280 \cr & 640 \times x = 1920 \times 28 \cr & \therefore x = 840 \cr} $$
Hence, second radio cp is 1920 - x
= 1920 - 840
= 1080
CP of both Radio = 840 and 1080
38. The reduction of Rs. 12 in the selling price of an article will changes 5% gain into $${\text{2}}\frac{1}{2}$$% lose. The cost price of the article is = ?
a) Rs. 140
b) Rs. 160
c) Rs. 80
d) Rs. 100
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{cost}}\,{\text{price}}\,{\text{be}}\,x \cr & {\text{gain}} = 5\% \cr & {\text{Selling}}\,{\text{Price}} = \frac{{105x}}{{100}} \cr & {\text{New}}\,{\text{SP}} = \frac{{105x}}{{100}} - 12 \cr & {\text{Now}}\,{\text{there}}\,{\text{is}}\,{\text{a}}\,{\text{loss}}\,{\text{of}}\,2.5\% \cr & x \times \frac{{100 - 2.5}}{{100}} = \frac{{105x}}{{100}} - 12 \cr & \frac{{97.5x}}{{100}} = \frac{{105x}}{{100}} - 12 \cr & 97.5x = 105x - 1200 \cr & 7.5x = 1200 \cr & \therefore x = 160 \cr} $$
39. An article was sold at a profit of 12% . If the cost price would be 10% less and selling price would be Rs. 5.75 more, there would be a profit of 30 %. Then at what price it should be sold to make a profit of 20% = ?
a) Rs. 115
b) Rs. 120
c) Rs. 138
d) Rs.215
Explanation: Let the CP1 of article = 100x
Initial SP1 = 100x + 12% of 100x = 100x + 12x = 112x
Now, If He brought article at 10% discount. Therefore CP2 = 90x
Now SP2 = 90x + 30% of 90x = 90x + 27x =117x
According to question
SP2 - SP1 = 5.75
⇒ 117x - 112x = 5.75
⇒ 5x = 5.75
⇒ x = $$\frac{5.75}{5}$$
⇒ x = 1.15
Initial Cost of article = 100 × 1.15 = Rs. 115
To sold article at 20% profit
= 115 + 20% of 115
= 115 + 23
= Rs. 138
40. By selling 90 ball pens for Rs. 160, a person loses 20% . How many ball pens should be sold for Rs. 96 so as to have a profit of 20% ?
a) 24
b) 36
c) 39
d) 42
Explanation:
$$\eqalign{ & {\text{S}}{\text{.P}}{\text{. of 90 ball pens}} \cr & = {\text{Rs}}{\text{. 160, loss}} = 20\% \cr & {\text{C}}{\text{.P}}{\text{.of 90 ball pens}} \cr & = {\text{Rs}}.\left( {\frac{{100}}{{80}} \times 160} \right) \cr & = {\text{Rs}}{\text{. }}200 \cr} $$
∴ Desired S.P. of 90 ball pens
$$\eqalign{ & = {\text{Rs}}.\left( {\frac{{120}}{{100}} \times 200} \right) \cr & = {\text{Rs}}{\text{. }}240 \cr} $$
For Rs. 240, ball pens sold = 90
For Rs. 96, ball pens sold
$$\eqalign{ & = \left( {\frac{{90}}{{240}} \times 96} \right) \cr & = 36 \cr} $$
41. If a man were to sell his handcart for Rs. 720, he would loss 25% . To gain 25% , the selling price is = ?
a) Rs. 960
b) Rs. 1200
c) Rs. 1000
d) Rs. 2100
Explanation Let cost price of hand cart = 100
According to the question,
\[{\text{100 (cp)}}\xrightarrow{{25\% {\text{Loss}}}}75{\text{ }}({\text{sp}})\xrightarrow{{ \times \frac{{48}}{5}}}720\,{\text{(given)}}\]
$$\eqalign{ & 75\,{\text{units}} \to 720 \cr & 1\,{\text{unit}} \to \frac{{720}}{{75}} = \frac{{48}}{5} \cr & 100\,{\text{units}} \to \frac{{48}}{5} \times 100 = 960 \cr & \therefore {\text{Cost price}} = {\text{ Rs}}{\text{.960}} \cr & {\text{To gain }}25\% {\text{ selling price is }} \cr & = {\text{cp}} + {\text{profit}}\% \times {\text{cp}} \cr & = 960 + \frac{{25}}{{100}} \times 960 \cr & = 960 + 240 = {\text{Rs}}{\text{.}}\,1200 \cr} $$
42. A grocery dealer cheats to the extent of 10% while buying as well as selling by using false weight. What is his increase in the profit percentage = ?
a) 20%
b) 21%
c) 22%
d) None of these
Explanation: According to the question,
Cheats while buying = 10%
Cheats while selling = 10%
$$\eqalign{ & \therefore \left( {a + b + \frac{{ab}}{{100}}} \right)\% \cr & = 10 + 10 + \frac{{10 \times 10}}{{100}} \cr & = 20 + 1 \cr & = 21 \cr} $$
∴ Increase in profit % = 21%
43. A book vendor sold a book at loss of 10% . Had he sold it for Rs. 108 more, he would have earned a profit of 10% . Find the cost of the book = ?
a) Rs. 442
b) Rs. 540
c) Rs. 648
d) Rs. 740
Explanation: Given loss = 10% profit = 10%
Difference of overall profit and loss = 10 - (-10) = 20%
20% of cp = sp
$$\frac{{20}}{{100}} \times {\text{cp = 108}}$$
20 × cp = 108 × 100
cp = $$\frac{{10800}}{{20}}$$
∴ cp = 540
44. By selling an article at some price, a man gains 10% . If the article is sold at twice of the price, the gain percent will be
a) 20%
b) 60%
c) 100%
d) 120%
Explanation:
$$\eqalign{ & {\text{Let C}}{\text{.P}}{\text{.}} = {\text{Rs}}.\,x. \cr & {\text{Then,}} \cr & {\text{S}}{\text{.P}}{\text{.}} = 110\% {\text{ of Rs}}.\,x. \cr & = {\text{Rs}}.\frac{{11x}}{{10}} \cr & {\text{New S}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {2 \times \frac{{11x}}{{10}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\frac{{11x}}{5} \cr & {\text{Gain}} = {\text{Rs}}.\left( {\frac{{11x}}{5} - x} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\frac{{6x}}{5} \cr & \therefore {\text{Gain}}\% = \left( {\frac{{6x}}{5} \times \frac{1}{x} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 120\% \cr} $$
45. If loss is $$\frac{1}{3}$$ of S.P., the loss percentage is
a) $$16\frac{2}{3}$$%
b) 20%
c) 25%
d) $$33\frac{1}{3}$$%
Explanation:
$$\eqalign{ & {\text{Let S}}{\text{.P}}{\text{.}} = {\text{Rs}}.\,x \cr & {\text{Then,}} \cr & {\text{Loss}} = {\text{Rs}}.\frac{x}{3} \cr & {\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {x + \frac{x}{3}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\frac{{4x}}{3} \cr & \therefore {\text{Loss }}\% \cr & = \left( {\frac{x}{3} \times \frac{3}{{4x}} \times 100} \right)\% \cr & = 25\% \cr} $$
46. A car worth Rs. 150000 was sold by x to y at 5% profit. y sold the car back to x at 2% loss. In the entire transaction = ?
a) x gained Rs. 4350
b) x lost Rs. 4350
c) x gained Rs. 3150
d) x lost Rs. 3150
Explanation: Money spent by x = Rs. 150000
Money received by x = 105% of Rs. 150000 = Rs. 157500
C.P. to x = 98% of Rs. 157500 = Rs. 154350
∴ x gains Rs. (157500 - 154350) = Rs. 3150
47. An article passing through two hands is sold at a profit of 38% at the original cost price. If the first dealer makes a profit of 20% , then the profit percent made by the second is
a) 5
b) 10
c) 12
d) 15
Explanation: Let the original cost of the article be Rs. P and the profit percent made by the second be x% .
Then,
120% of (100 + x)% of P = 138% of P
$$\eqalign{ & \Rightarrow \frac{{120}}{{100}} \times \frac{{\left( {100 + x} \right)}}{{100}} = \frac{{138}}{{100}} \cr & \Rightarrow \frac{{100 + x}}{{100}} = \frac{{23}}{{20}} \cr & \Rightarrow 100 + x = 115 \cr & \Rightarrow x = 15 \cr} $$
48. A dealer buys an article listed at Rs. 100 and gets successive discount of 10% and 20% . He spends 10% of the cost price on transportation. At what price should he sell the article to earn a profit of 15% ?
a) Rs. 90.80
b) Rs. 92.00
c) Rs. 91.20
d) Rs. 91.08
Explanation: A dealer buys an article listed at Rs 100 and gets successive discounts of 10% and 20%.
Cost After 10% discount = 100 – 10% of 100
= 100 - 10 = 90
Cost After 20% discount = (90 – 20% of 90
= 90 - 18 = 72
He spends 10% of the cost price on transportation.
∴ Total cost = 72 + 10% of 72
= 72 + 7.2
= 79.2
He wants to make a profit of 15%
∴ SP = 79.2 + 15% of 79.2
= 79.2 + $$\frac{{15}}{{100}}$$ × 79.2
= 79.2 + 11.88
= Rs. 91.08
49. Allowing 20% and 15% successive discounts, the selling price of an article becomes Rs. 3060: then the marked price will be = ?
a) Rs. 4400
b) Rs. 5000
c) Rs. 4500
d) Rs. 4000
Explanation:
$$\eqalign{ & {\text{Total discount }}\% \cr & {\text{ = }}\left( {20 + 15 - \frac{{20 \times 15}}{{100}}} \right)\% \cr & = 35 - 3 \cr & = 32\% \cr & = \frac{{32 \to {\text{Discount}}}}{{100 \to {\text{MRP}}}} \cr} $$
MRP → Discount → Selling Price
100 → 32 → 68
68 units → 3060
1 units → 45
⇒ then MRP = 100 units
= 45 × 100 = Rs. 4500
50. List price of a book is Rs. 100. A dealer sells three such books for Rs. 274.50 after allowing discount at a certain rate, find the rate of discount = ?
a) 8.33%
b) 8.16%
c) 8.50%
d) 8.34%
Explanation: Given,
= MRP of book = Rs. 100
= Selling price of 3 books = Rs. 274.50
= Selling price of 1 book = Rs. 91.50
Discount on each book
= 100 - 91.50 = Rs. 8.50
Therefore discount %
$$\eqalign{ & = \frac{{8.50}}{{100}} \times 100\,\% \cr & = 8.50\,\% \cr} $$
51. By selling 33 meters of cloth a person gains the cost price of 11 meters. Find his gain % = ?
a) $$33\frac{1}{3}\% $$
b) $$33\frac{1}{2}\% $$
c) $$33\% $$
d) $$34\frac{1}{3}\% $$
Explanation Let Selling price of 1 meters cloth = Rs. 1
Selling price of 33 meters cloth = Rs. 33
Cost price of 1 meter cloth = Rs. x
Cost price of 33 meters cloth = Rs. 33x
According to the question,
Profit = Selling price - Cost price
$$\eqalign{ & \Rightarrow 11x = 33 - 33x \cr & \Rightarrow 44x = 33 \cr & \Rightarrow x = \frac{{33}}{{44}} = \frac{3}{4} \cr & {\text{Cost price of 1 metre}} \cr & = {\text{Rs}}{\text{.}}\frac{3}{4} \cr & {\text{Cost price of 33 metres}} \cr & = \frac{3}{4} \times 33 \cr & = {\text{Rs}}.\frac{{99}}{4} \cr} $$
Selling price of 33 meters = Rs. 33
Profit = Selling price = Cost price
$$\eqalign{ & = 33 - \frac{{99}}{4} \cr & = \frac{{33}}{4} \cr & \therefore {\text{Profit }}\% \cr & {\text{ = }}\frac{{\frac{{33}}{4}}}{{\frac{{99}}{4}}} \times 100 \cr & = \frac{{33}}{{99}} \times 100 \cr & = \frac{1}{3} \times 100 \cr & = 33\frac{1}{3}\% \cr} $$
52. A cloth merchant on selling 33 meters of cloth obtains a profit equal to the selling price of 11 meters of cloth the profit is = ?
a) 40%
b) 11%
c) 50%
d) 22%
Explanation: Let the selling price of 1 meter cloth = Rs. 1
The Selling price of 33 meters cloth
= 1 × 33 = Rs. 33
Cost of 1 meter cloth = Rs. x
Cost price 33 meters cloth = x × 33 = Rs. 33x
According to the question,
Profit = Selling price - Cost price
$$\eqalign{ & \Rightarrow 11 = 33 - 33x \cr & \Rightarrow 33x = 22 \cr & \Rightarrow x = \frac{{22}}{{33}} = \frac{2}{3} \cr} $$
Cost price of 1 meter cloth $$ = {\text{Rs}}{\text{.}}\frac{2}{3}$$
Cost price of 33 meters cloth
$$\eqalign{ & = \frac{2}{3} \times 33 \cr & = {\text{Rs}}.22 \cr} $$
Selling price of 33 meters cloth = Rs. 33
Profit = Selling price - Cost price
= 33 - 22 = 11
$$\eqalign{ & {\text{Profit}}\% \cr & = \frac{{11}}{{22}} \times 100 \cr & = 50\% \cr} $$
53. An item costing Rs. 840 was sold by a shopkeeper at a gain of 10% and it was again sold by the new buyer at a loss of 5%. Find selling price of the item is = ?
a) Rs. 877.80
b) Rs. 798
c) Rs. 924
d) Rs. 37.80
Explanation:According to the question,
Cost price = Rs. 840
10% Profit on cost price
$$\eqalign{ & = \frac{{10}}{{100}} \times 840 \cr & = {\text{Rs}}{\text{. }}84 \cr & \therefore {\text{Selling price}} \cr & = 840 + 84 \cr & = {\text{Rs}}{\text{. 924}} \cr} $$
New buyer cost price
$$ = {\text{Rs}}{\text{. 924}}$$
5% loss on Cost price
$$\eqalign{ & = \frac{5}{{100}} \times 924 \cr & = {\text{Rs}}{\text{. }}46.2 \cr & {\text{Selling price}} \cr & = {\text{Rs}}{\text{. 924}} - 46.2 \cr & = {\text{Rs}}{\text{. }}877.80 \cr} $$
54. The cost of raw materials of a product increases by 30%, the manufacturing cost increases by 20% and the selling price of the product increases by 60%. The raw material and the manufacturing cost originally formed 40% and 60% of the total cost respectively. If the original profit percentage was one - fourth the original manufacturing cost, find the approximate new profit percentage
a) 48.39%
b) 54.76%
c) 63.85%
d) 66.75%
Explanation: Let the total initial cost of production be Rs. 100
Then,
manufacturing cost = Rs. 60
Cost of raw materials = Rs. 40
Original Selling Price
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {100 + \frac{{60}}{4}} \right) \cr & = {\text{Rs}}{\text{. }}115 \cr} $$
New cost of raw materials = 130% of Rs. 40 = Rs. 52
New Manufacturing cost = 120% of Rs. 60 = Rs. 72
New cost of the product = Rs. (52 + 72) = Rs. 124
New S.P. = 160% of Rs. 115
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {\frac{{160}}{{100}} \times 115} \right) \cr & = {\text{Rs}}{\text{. }}184 \cr} $$
New profit = Rs. (184 - 124) = Rs. 60
$$\eqalign{ & \therefore {\text{New profit }}\% \cr & = \left( {\frac{{60}}{{124}} \times 100} \right)\% \cr & = 48.39\% \cr} $$
55. Previously, the manufacturing cost of a product was thrice the cost of raw
material. Now the cost of raw material increases in the ratio 5 : 12 and manufacturing cost increases in the ratio of 3 : 5. The previous cost of the product was Rs. 8. What should be the present selling price so that 25% profit can be made?
a) Rs. 13.70
b) Rs. 14.80
c) Rs. 18.50
d) Rs. 19.50
Explanation: Original C.P. of the product = Rs. 8.
Original manufacturing cost
$$\eqalign{ & = {\text{Rs}}.\left( {\frac{3}{4} \times 8} \right) \cr & = {\text{Rs}}{\text{. }}6 \cr} $$
Original cost of raw material
$$\eqalign{ & = {\text{Rs}}.\left( {8 - 6} \right) \cr & = {\text{Rs}}{\text{. }}2 \cr} $$
New manufacturing cost
$$\eqalign{ & = {\text{Rs}}.\left( {\frac{5}{3} \times 6} \right) \cr & = {\text{Rs}}{\text{. }}10 \cr} $$
New cost of raw material
$$\eqalign{ & = {\text{Rs}}.\left( {\frac{{12}}{5} \times 2} \right) \cr & = {\text{Rs}}{\text{. }}\frac{{24}}{5} \cr} $$
New S.P. of the product
$$\eqalign{ & = {\text{Rs}}.\left( {10 + \frac{{24}}{5}} \right) \cr & = {\text{Rs}}{\text{. }}\frac{{74}}{5} \cr} $$
$$\eqalign{ & \therefore {\text{Desired S}}{\text{.P}}{\text{.}} \cr & = 125\% {\text{ of Rs}}.\frac{{74}}{5} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{125}}{{100}} \times \frac{{74}}{5}} \right) \cr & = {\text{Rs}}.18.50 \cr} $$
56.If the total cost of 73 articles having equal cost is Rs. 5110 and the total selling price of 89 such articles is Rs. 5607, then in the transaction, there will be = ?
a) A loss of 15%
b) A gain of 10%
c) A loss of 10%
d) A gain of 15%
Explanation: According to the question,
Cost price of 73 articles are
= Rs. 5110
Cost price of 1 articles are
$$\eqalign{ & = \frac{{5110}}{{73}} \cr & = {\text{Rs}}{\text{. 70}} \cr} $$
Selling price of 89 articles are = Rs. 5607
Selling price of 1 articles is
$$\eqalign{ & = \frac{{5607}}{{89}} \cr & {\text{ = Rs}}{\text{. 63}} \cr} $$
Loss = Cost price - Selling price
Loss = 70 - 63 = Rs. 7
$$\eqalign{ & {\text{Loss}}\% = \frac{7}{{70}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10\% \cr} $$
57.A man bought oranges at the rate of 8 for Rs. 34 and sold them at the rate of 12 for Rs. 57. How many oranges should be sold to earn a net profit of Rs. 45 ?
a) 90
b) 100
c) 135
d) 150
Explanation: CP of 1 orange $$ = {\text{Rs}}{\text{.}}\,\frac{{34}}{8} = {\text{Rs}}{\text{.}}\,4.25$$
SP of 1 orange $$ = {\text{Rs}}{\text{.}}\,\frac{{57}}{{12}} = {\text{Rs}}{\text{.}}\,4.75$$
Profit on each apple = (4.75 - 4.25) = Rs. 0.50
∴ Number of apples required $$ = \frac{{45}}{{0.50}} = 90$$
58.A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity (in kg) sold at 18% profit is.
a) 400
b) 560
c) 600
d) 640
Explanation: Let the quantity sold at 18% profit be $$x$$ kg and let C.P. per kg be Rs. 1
Then,
quantity sold at 8% profit = (1000 - $$x$$) kg.
Total C.P. = Rs. 1000
Total S.P. = Rs. [108% of (1000 - x) + 118% of $$x$$]
$$ = {\text{Rs}}.\left[ {\frac{{27}}{{25}}\left( {1000 - x} \right) + \frac{{59x}}{{50}}} \right]$$ $$ = {\text{Rs}}.\left( {1080 + \frac{x}{{10}}} \right)$$
$$\eqalign{ & \therefore 1080 + \frac{x}{{10}} = 114\% {\text{ of }}1000 \cr & \Rightarrow 1080 + \frac{x}{{10}} = 1140. \cr & \Rightarrow \frac{x}{{10}} = 60 \cr & \Rightarrow x = 600 \cr} $$
59.Two - thirds of a consignment was sold at a profit of 6% and the rest at a loss of 3%. If however there was an overall profit of Rs. 540, the value of consignment was
a) Rs. 15000
b) Rs. 16000
c) Rs. 18000
d) None of these
Explanation: Let the total value be Rs. x
$$\eqalign{ & {\text{value of }}\frac{2}{3}{\text{rd}} = {\text{Rs}}{\text{.}}\frac{{2x}}{3} \cr & {\text{value of}}\frac{1}{3}{\text{rd}} = {\text{Rs}}.\frac{x}{3} \cr & {\text{Total S}}{\text{.P}}{\text{.}} \cr & = {\text{Rs}}.\left[ {\left( {106\% {\text{ of }}\frac{{2x}}{3}} \right) + \left( {97\% {\text{ of }}\frac{x}{3}} \right)} \right] \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{53x}}{{75}} + \frac{{97x}}{{300}}} \right) \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{309x}}{{300}}} \right) \cr & \therefore \frac{{309x}}{{300}} - x = 540 \cr & \Rightarrow \frac{{9x}}{{300}} = 540 \cr & \Rightarrow x = \left( {\frac{{540 \times 300}}{9}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 18000 \cr} $$
60. Krishna purchased a number of articles at Rs. 10 for each and the same number for Rs. 14 each. He mixed them together and sold them for Rs. 13 each. Then his gain or loss percent is = ?
a) Loss $$8\frac{1}{3}\% $$
b) Gain $$8\frac{2}{3}\% $$
c) Loss $$8\frac{2}{3}\% $$
d) Gain $$8\frac{1}{3}\% $$
Explanation: Let article purchased be 1
1 articale = Rs. 10
1 articale = Rs. 14
CP of 2 article = 10 + 14 = Rs. 24
CP of 1 article = $$\frac{{24}}{2}$$ = Rs. 12
SP of 1 article = Rs. 13
Profit = 13 - 12 = Rs. 1
$$\eqalign{ & {\text{Profit}}\% = \frac{1}{{12}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{25}}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 8\frac{1}{3}\% \cr} $$
61. By selling an article at $$\frac{2}{3}$$ of the marked price, there is a loss of 10% . The profit percent, when the article is sold at the marked price, is
a) 20%
b) 30%
c) 35%
d) 40%
Explanation:
$$\eqalign{ & {\text{Let the M}}{\text{.P be Rs}}{\text{. }}x. \cr & {\text{Then,}} \cr & {\text{S}}{\text{.P}}{\text{.}} = {\text{Rs}}.\frac{2}{3}x,{\text{loss}} = 10\% \cr & {\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {\frac{{100}}{{90}} \times \frac{2}{3}x} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\frac{{20}}{{27}}x \cr & {\text{If an article is sold at M}}{\text{.P}}{\text{.}} \cr & {\text{Then,}} \cr & {\text{Profit}} = {\text{Rs}}.\left( {x - \frac{{20}}{{27}}x} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\frac{{7x}}{{27}} \cr & \therefore {\text{Profit}}\% \cr & = \left( {\frac{{7x}}{{27}} \times \frac{{27}}{{20x}} \times 100} \right)\% \cr & = 35\% \cr} $$
62. Raghavan purchase a scooter at $$\frac{13}{15}$$ of its selling price and sold it at 12% more than its selling price. His gain is
a) 20%
b) $$29\frac{3}{{13}}$$%
c) 30%
d) $$38\frac{1}{{13}}$$%
Explanation:
$$\eqalign{ & {\text{Let S}}{\text{.P}}{\text{. be Rs}}{\text{. }}x \cr & {\text{Then,}} \cr & {\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}.\frac{{13}}{{15}}x, \cr & {\text{Receipt}} = 112\% {\text{ of Rs}}{\text{. }}x \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\frac{{28}}{{25}}x \cr & {\text{Gain}} = {\text{Rs}}.\left( {\frac{{28x}}{{25}} - \frac{{13x}}{{15}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\frac{{19x}}{{75}} \cr & \therefore {\text{Gain}}\% \cr & = \left( {\frac{{19x}}{{75}} \times \frac{{15}}{{13x}} \times 100} \right)\% \cr & = \frac{{380}}{{13}}\% \cr & = 29\frac{3}{{13}}\% \cr} $$
63.A sells a bicycle to B at a profit of 20% . B sells it to C at a profit of 25% . If C pays Rs. 225 for it, the cost price of the bicycle for A is = ?
a) Rs. 110
b) Rs. 125
c) Rs. 120
d) Rs. 150
Explanation: According to the question,
| A | B | C | |||
| 10 | \[\xrightarrow{{20\% {\text{ profit}}}}\] | 12 | \[\xrightarrow{{25\% {\text{ profit}}}}\] | 12 + 3 | = 15 \[ \to \] 225 |
$$\eqalign{ & \therefore {\text{1 unit}} = {\text{15}} \cr & \therefore {\text{10 units}} = 10 \times 15 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.150}} \cr} $$
64. A house worth Rs. 150000 is sold by X at a 5% profit to Y, Y sells the house back to X at a 2% loss. Then find profit and loss in the entire transaction = ?
a) X gains Rs. 4150
b) X loses Rs. 4150
c) X gains Rs. 3150
d) X loses Rs. 3150
Explanation: Money spent by X = Rs. 150000
Money received by X = 105% of Rs. 150000 = Rs. 157500
C.P. to X = 98% of Rs. 157500 = Rs. 154350
∴ X gains Rs. (157500 - 154350) = Rs. 3150
65. A manufacturer sells an article to a wholesale dealer at a profit of 10% . The wholesale dealer sells it to a shopkeeper at 20% profit. The shop - keeper sells it to a customer for Rs. 56100 at a loss of 15% . Then the cost price of the article to the manufacturer is = ?
a) Rs. 25000
b) Rs. 10000
c) Rs. 50000
d) Rs. 55000
Explanation:
$$\eqalign{ & = \left( {\frac{{56100 \times 100 \times 100 \times 100}}{{\left( {100 - 15} \right) \times \left( {100 + 10} \right) \times \left( {100 + 20} \right)}}} \right) \cr & = \left( {\frac{{56100 \times 100 \times 100 \times 100}}{{85 \times 110 \times 120}}} \right) \cr & = {\text{Rs}}{\text{.}}\,50000 \cr} $$
66. A man purchases some oranges at the rate of 3 for Rs. 40 and the same quantity at 5 for Rs. 60. If he sells all the oranges at the rate of 3 for Rs. 50, find his gain or loss percent ( to the nearest integer ) = ?
a) 34% loss
b) 31% profit
c) 31% loss
d) 32% profit
Explanation: Man purchased 15 oranges of each type
CP of 1st type $$ = \frac{{40}}{3} \times 15 = 200$$
CP of 2nd type $$ = \frac{{60}}{5} \times 15 = 180$$
Total cost price = (200 + 180) = 380
Total selling price $$ = \frac{{50}}{3} \times 30 = 500$$
∴ Profit percentage
$$\eqalign{ & = \frac{{500 - 380}}{{380}} \times 100 \cr & = \frac{120}{380}\times100 \cr & = \frac{600}{19}\% \cr & = 31.57\% \cr & \approx 32\% \cr} $$
67. Nikita bought 30 kg of wheat at the rate of Rs. 9.50 per kg of wheat and the same amount of wheat at the rate Rs. 8.50 per kg and mixed them. She sold the mixture at the rate of Rs. 8.90 per kg. Her total profit or loss in the transaction was = ?
a) Rs. 2 loss
b) Rs. 2 profit
c) Rs. 6 loss
d) Rs. 6 profit
Explanation: According to the question
Cost Price
= 30 × 9.50 + 30 × 8.50
= 30[9.50 + 8.50]
= 30 × 18
= Rs. 540
Selling Price
= 60 × 8.90
= Rs. 534
Loss = Cost price - Selling price
= 540 - 534
= Rs. 6
68. Albert buys 4 horses and 9 cows for Rs. 13400. If he sells the horses at 10% profit and the cows at 20% profit, then he earns a total profit of Rs. 1880. The cost of a horse is
a) Rs. 1000
b) Rs. 2000
c) Rs. 2500
d) Rs. 3000
Explanation: Let C.P. of each horse be Rs. x and C.P. of each cow be Rs. y.
Then,
= 4x + 9y = 13400 ......(i)
and,
10% of 4x + 20% of 9y = 1880
$$\eqalign{ & \Rightarrow \frac{2}{5}x + \frac{9}{5}y = 1880 \cr & \Rightarrow 2x + 9y = 9400....({\text{ii}}) \cr} $$
Solving (i) and (ii), we get:
x = 2000 and y = 600
∴ Cost price of each horse = Rs. 2000
69. A man purchases two clocks A and B at a total cost of Rs. 650. He sells A with 20% profit and B at a loss of 25% and gets the same selling price for both the clocks. What are the purchasing prices of A and B respectively ?
a) Rs. 225, Rs. 425
b) Rs. 250, Rs. 400
c) Rs. 275, Rs. 375
d) Rs. 300, Rs. 350
Explanation: Let C.P. of clock A be Rs. x and that of clock B be Rs. (650 - x).
Then,
120% of x = 75% of (650 - x)
$$\eqalign{ & \Rightarrow 650 - x = \frac{{120}}{{75}}x \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{8}{5}x \cr & \Rightarrow \frac{{13}}{5}x = 650 \cr & \Rightarrow x = \left( {\frac{{650 \times 5}}{{13}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 250 \cr & \therefore {\text{C}}{\text{.P}}{\text{. of A}} = {\text{Rs}}{\text{. }}250 \cr & {\text{C}}{\text{.P}}{\text{. of B}} = {\text{Rs}}{\text{. }}400 \cr} $$
70.Nita blends two varieties of tea one costing Rs. 180 per kg and another costing Rs. 200 per kg in the ratio 5 : 3. If she sells the blended variety at Rs. 210 per kg then her gain is = ?
a) 110%
b) 11%
c) 12%
d) 13%
Explanation: Let 5 kg of cheaper be mixed with 3 kg of dearer.
Then,
Total CP = Rs. (180 x 5 + 200 x 3) = Rs. 1500
Total SP = Rs. (210 x 8) = Rs. 1680
$$\eqalign{ & {\text{Gain}}\% = \left( {\frac{{180}}{{1500}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 12\% \cr} $$
71. To gain 10% on selling the mixture of milk and water at the cost price of pure milk, the quantity of water to be mixed with 50 kg of pure milk is = ?
a) 2.5 kg
b) 5 kg
c) 7.5 kg
d) 10 kg
Explanation: Let cost price of 1 kg = Rs. 1
Cost price of 50 kg = Rs. 50
$$\eqalign{ & \Rightarrow {\text{Profit}} = \frac{{10}}{{100}} \times {\text{50}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 5}} \cr & \therefore {\text{Quantity to added}} \cr & = \frac{5}{1} = {\text{5 kg}} \cr} $$
72. A milkman bought 70 litres of milk for Rs. 630 and added 5 litres of water. If sells it at Rs. 9.00 per litres, his profit percentage is = ?
a) $$8\frac{1}{5}$$%
b) 7%
c) $$8\frac{2}{5}$$%
d) $$7\frac{1}{7}$$%
Explanation: According to the question,
Cost price of 70 litres of milk = Rs. 630
Added 5 litres of water
Now, the solution becomes = 75 litres
Cost price of water = Rs. 0
∴ Selling price of 1 litre milk = Rs. 9
Selling price of 75 litres milk = 9 × 75 = Rs. 675
Profit = Selling price - Cost price
= 675 - 630
= 45
$$\eqalign{ & {\text{Profit}} = \frac{{\operatorname{Profit} }}{{{\text{Cost price}}}} \times 100 \cr & = \frac{{45}}{{630}} \times 100 \cr & = \frac{{50}}{7} \cr & = 7\frac{1}{7}\% \cr} $$
73. A farmer sold a cow and an ox for Rs. 800 and got a profit of 20% on the cow and 25% on the ox. If he sells the cow and the ox for Rs. 820 he gets a profit of 25% on the cow and 20% on the ox. The individual cost price of the cow and the ox is :
a) Rs. 530.60, Rs. 130.60 (approx)
b) Rs. 515.60, Rs. 115.60 (approx)
c) Rs. 531.50, Rs. 135.60 (approx)
d) Cannot be determined
Explanation: Let the C.P. of the cow be Rs. x and that of the ox be Rs. y
Then,
= 120% of x + 125% of y = 800
$$ \Rightarrow \frac{{6x}}{5} + \frac{{5y}}{4} = 800$$
⇒ 24x + 25y = 16000 .......(i)
And
125% of x + 120% of y = 820
$$ \Rightarrow \frac{{5x}}{4} + \frac{{6y}}{5} = 820$$
⇒ 25x + 24y = 16400 ......(ii)
Adding (i) and (ii), we get :
49x + 49y = 32400
$$ \Rightarrow x + y = \frac{{32400}}{{49}}......(iii)$$
Substracting (i) from (ii), we get :
x - y = 400 ........(iv)
Adding (iii) and (iv), we get :
$$\eqalign{ & 2x = \frac{{32400}}{{49}} + 400 \cr & \,\,\,\,\,\,\,\,\, = \frac{{52000}}{{49}} \cr & \Rightarrow x = \frac{{26000}}{{49}} \approx 530.60 \cr & {\text{Putting }}x = \frac{{26000}}{{49}}{\text{ in }}(iii), \cr & {\text{we get}}: \cr & y = \frac{{32400}}{{49}} - \frac{{26000}}{{49}} \cr & \,\,\,\,\,\, = \frac{{6400}}{{49}} \approx 130.60 \cr} $$
74. The C.P. of two watches taken together is Rs. 840. If by selling one at a profit of 16% and the other at a loss of 12% , there is no loss or gain in the whole transaction, then the C.P. of the two watches are respectively.
a) Rs. 360, Rs. 480
b) Rs. 480, Rs. 360
c) Rs. 380, Rs. 460
d) Rs. 400, Rs. 440
Explanation: C.P. = Cost Price.
Let the C.P. of the watches be Rs. x and Rs. (840 - x)
∴ (116% of x) + [88% of (840 - x)] = 840
⇒ 116x + 73920 - 88x = 84000
⇒ 28x = 10080
⇒ x = 360
∴ Their cost prices are Rs. 360 and Rs. 480
75. A space research company wants to sell its two products A and B. If the product A is sold at 20% loss and the product B at 30% gain, the company will not lose anything. If the product A is sold at 15% loss and the product B at 15% gain, the company will lose Rs. 6 million in the deal. What is the cost of product B ?
a) Rs. 80 million
b) Rs. 100 million
c) Rs. 120 million
d) Rs. 140 million
Explanation: Let the cost of product A be Rs. x and B be Rs. y
According to first sell
0.80x + 1.3y = x + y
⇒ 0.2x = 0.3y
⇒ x = $$\frac{3\text{y}}{2}$$ . . . . . . (i)
According to second sell
0.85x + 1.15y = (x + y) - 6
⇒ 0.15y = 0.15x - 6 (Multiply by 100)
⇒ 15y = 15x - 600 (Putting the value of x)
⇒ 15y = 15 × $$\frac{3\text{y}}{2}$$ - 600
⇒ 15y = $$\frac{45\text{y}}{2}$$ - 600 (Multiply by 2 both side)
⇒ 30y = 45y - 1200
⇒ 15y = 1200
⇒ y = 80 million
76. An increase of Rs. 3 in the selling price of an article turns a loss of $$7\frac{1}{2}$$% into a gain of $$7\frac{1}{2}$$%. The cost price in (Rs.) of the article is
a) 10
b) 15
c) 20
d) 25
Explanation:
$$\eqalign{ & {\text{Let C}}{\text{.P}}{\text{. be Rs}}{\text{. }}x \cr & {\text{Then,}} \cr & 107\frac{1}{2}\% {\text{ of }}x - 92\frac{1}{2}\% {\text{ of }}x = 3 \cr & \Rightarrow \frac{{215}}{{200}}x - \frac{{185}}{{200}}x = 3 \cr & \Rightarrow \frac{{30x}}{{200}} = 3 \cr & \Rightarrow x = 20 \cr} $$
77. A shopkeeper sells an article at $$12\frac{1}{2}$$% loss. If he sells it for Rs. 92.50 more than he gains 6% . What is the cost price of the article ?
a) Rs. 500
b) Rs. 510
c) Rs. 575
d) Rs. 600
Explanation:
$$\eqalign{ & {\text{Let C}}{\text{.P}}{\text{. be Rs}}{\text{. }}x \cr & {\text{Then,}} \cr & {\text{ = }}\left( {106\% {\text{ of }}x} \right) - \left( {87\frac{1}{2}\% {\text{ of }}x} \right) = 92.50 \cr & \Rightarrow 18\frac{1}{2}\% {\text{ of }}x = 92.50 \cr & \Rightarrow x = \left( {\frac{{92.50 \times 100 \times 2}}{{37}}} \right) = 500 \cr & {\text{CP}} = {\text{Rs}}{\text{. }}500 \cr} $$
78. A sells a cycle to B at a profit of 10% , B sells to C at a profit of 20% . If C pays Rs. 264 for it, how much did A pay for it ?
a) Rs. 200
b) Rs. 220
c) Rs. 225
d) Rs. 234
Explanation: Let cost price for A = Rs. 100
SP for A = CP for B = 100 + 10% of 100 = 110
SP for B = CP for C = 110 + 20% of 110 = 132
Given,
CP for C = 264
So,
132 = 264
$$\eqalign{ & 1 = \frac{{264}}{{132}} \cr & 100 = \frac{{264 \times 100}}{{132}} = {\text{Rs}}{\text{.}}\,200 \cr} $$
CP for A = Rs. 200
79. A sold a tape - recorder to B for Rs. 4860 at a loss of 19% . Again B sold it to C at price that would give A a profit of 17% . The gain of B is = ?
a) $$22\frac{2}{9}\% $$
b) $$33\frac{1}{3}\% $$
c) $$44\frac{4}{9}\% $$
d) $$66\frac{2}{3}\% $$
Explanation: CP of the Product = $$\frac{{4860 \times 100}}{{81}} = 6000$$
Loss of A = 6000 - 4860 = 1140
Now B sold the product to C with 17% profit of A
i.e. 6000 + 17% of 6000
= 6000 + 1020
= 7020
∴ Total Profit of B = 7020 - 4860 = 2160
% Gain of B $$ = \frac{{2160}}{{4860}} \times 100 = 44\frac{4}{9}\% $$
80.A dishonest fruit vendor sells his goods at cost price but they uses a weight of 900 gm. for the 1 kg. weight. His gain percent is = ?
a) 12%
b) $$11\frac{1}{9}$$%
c) $$10\frac{1}{9}$$%
d) 10%
Explanation: According to the question,
Shopkeeper sells his goods at cost price
Let, Cost price of 1000 gm. goods = Rs. 1000
He sold 900 gm. goods
Selling price of 900 gm. goods = Rs. 1000
Cost price of 900 gm. goods = Rs. 900
$$\eqalign{ & {\text{Profit}}\% = \frac{{100}}{{900}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 11\frac{1}{9}\% \cr} $$
81. A person sells an article for Rs. 75 and gains as much percent as the cost price of the article in rupees. The cost price of the article is = ?
a) Rs. 37.50
b) Rs. 40
c) Rs. 50
d) Rs. 150
Explanation In this type of question go through option
Option : C
Cost price = Rs. 50
Gains as much percentage as the cost price of the article means 50% gains
50% of cost price
50% of Rs. 50 = Rs. 25
Selling price = Cost price + Profit
Selling price = 50 + 25
Selling price = Rs. 75
82.A clock was sold for Rs. 144. If the percentage of profit was numerically equal to the cost price the cost of the clock was = ?
a) Rs. 72
b) Rs. 80
c) Rs. 90
d) Rs. 100
Explanation: According to the question,
Selling price = Rs. 144
Cost price is equal to percentage of profit.
Note : In this type of question go through option.
Option = B
Cost price = Rs. 80
Profit % = 80%
Selling price
$$\eqalign{ & = 80 + \frac{{80}}{{100}} \times 80 \cr & = {\text{Rs}}{\text{.144 (Satisfied)}} \cr} $$
83. If the price of eraser is reduced by 25%. A person can buy 2 more erasers for a rupee. How many erasers are available for a rupee after reduction ?
a) 8
b) 6
c) 4
d) 2
Explanation: Let n erasers be available for a rupee
Reduced Price $$ = \frac{{75}}{{100}} \times 1 = \,\frac{3}{4}$$
$$\frac{3}{4}$$ rupee fetch n erasers = 1 Rupee will fetch $$\left( {{\text{n}} \times \frac{4}{3}} \right)$$ erasers
Therefore,
$$\eqalign{ & \frac{{4n}}{3} = n + 2 \cr & \Rightarrow 4n = 3n + 6 \cr & \Rightarrow n = 6 \cr} $$
Now total number of erasers are available for a rupee = 6 + 2 =8
84. If a company sells a car with a marked price of Rs. 272000 and gives a discount of 4% on Rs. 200000 and 2.5% on the remaining amount of Rs. 72,000, then the actual price charged by the company for the car is
a) Rs. 2,50,000
b) Rs. 2,55,000
c) Rs. 2,60,000
d) Rs. 2,62,200
Explanation: M.P. = Rs. 272000
Discount = Rs. [(4% of 200000) + (2.5% of 72000)]
= Rs. (8000 + 1800)
= Rs. 9800
Actual price
= Rs. (272000 - 9800)
= Rs. 2,62,200
85. An umbrella marked at Rs. 80 is sold for Rs. 68. The following rate of discount is:
a) 15%
b) 17%
c) 18.5%
d) 20%
Explanation:
$$\eqalign{ & {\text{Rate of discount}} \cr & = \left( {\frac{{12}}{{80}} \times 100} \right)\% \cr & = 15\% \cr} $$
86. A milkman makes 20% profit by selling milk mixed with water at Rs. 9 per litre, if the cost price of 1 litre pure milk is Rs. 10, then the ratio of milk and water in the said mixture is = ?
a) 3 : 1
b) 4 : 1
c) 3 : 2
d) 4 : 3
Explanation: According to question,
S.P. at 20% profit = Rs. 9/litres
Cost of mixture $$ = \frac{9}{{120}} \times 100 = {\text{Rs}}{\text{.}}\,7.5/{\text{litre}}$$
Now, let the ratio of milk and water in the mixture = x : y
$$\eqalign{ & \Rightarrow \frac{{\left( {10 \times x} \right) + \left( {0 \times y} \right)}}{{x + y}} = 7.5 \cr & \Rightarrow 10x = 7.5\left( {x + y} \right) \cr & \Rightarrow x:y = 3:1 \cr} $$
87. A shopkeeper bought 15 kg of rice at the rate of Rs. 29 per kg and 25 kg of rice at the rate of Rs. 20 per kg. He sold the mixture of both types of rice at the rate of Rs. 27 per kg. His profit in this transaction is = ?
a) Rs. 125
b) Rs. 140
c) Rs. 150
d) Rs. 145
Explanation: According to the question,
Cost price of mixture of rice
= 15 × 29 + 25 × 20
= 435 + 500
= Rs. 935
Selling price of 1 kg mixture of rice = Rs. 27
Selling price of 40 kg mixture of rice
= 27 × 40 = Rs. 1080.
Profit = Selling price - Cost price
= 1080 - 935
= Rs. 145
88. On selling 17 balls at Rs. 720 there is a loss equal to the cost price of 5 balls. The cost price of a ball is = ?
a) Rs. 45
b) Rs. 50
c) Rs. 60
d) Rs. 55
Explanation:According to the question,
Let cost price of 1 ball is = Rs. x
∴ Cost price - Selling price = Loss
17x - 720 = 5x
12x = 720
⇒ x = 60
∴ Cost price of 1 ball is Rs. 60
89. A small and medium enterprise imports two components A and B from Taiwan and China respectively and assembles them with other components to form a toy. Components A contributes to 10% of production cost while components B contributes to 20% of production cost. Usually the company sells this toy at 20% above the production cost. Due to increase in the raw material and labour cost in both the countries ,component A became 20% costlier and components B became 40% costlier. Owing to these reasons the company increased its selling price by 15%. Considering that cost of other components does not change. What will be the profit percentage if the toy is sold at the new price?
a) 15.5%
b) 25.5%
c) 35.5%
d) 40%
Explanation: Let the original cost of the toy be Rs. 100.
Then,
Original cost of component A
= 10% of Rs. 100
= Rs. 10
Original cost of component B
= 20% of Rs. 100
= Rs. 20
Original S.P. of the toy
= 120% of Rs. 100
= Rs. 120
New cost of component A
= 120% of Rs. 10
= Rs. 12
New cost of component B
= 140% of Rs. 20
= Rs. 28
New price of the toy
= Rs. [100 + (12 + 28) - (10 + 20)]
= Rs. 110
New S.P. of the toy
= 115% of Rs. 120
= Rs. 138
Profit = Rs. ( 138 - 110) = Rs. 28
$$\eqalign{ & \therefore {\text{Profit }}\% = \left( {\frac{{28}}{{110}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 25.45\% \approx 25.5\% \cr} $$
90. A firm of readymade garments makes both men's and women's shirts. Its average profit is 6% of the sales. Its profit in men's shirt average 8% of the sales and women's shirts comprise 60% of the output. The average profit per sales rupee in women's shirts is
a) 0.0166
b) 0.0466
c) 0.0666
d) None of these
Explanation: Let the total sales be Rs. x and let the profit in women's shirts average y% of the sales.
Then,
= 8% of 40% of x + y% of 60% of x = 6% of x
$$\eqalign{ & \Rightarrow \frac{8}{{100}} \times \frac{{40}}{{100}} \times x + \frac{y}{{100}} \times \frac{{60}}{{100}} \times x = \frac{6}{{100}} \times x \cr & \Rightarrow \frac{{32}}{{10}} + \frac{{6y}}{{10}} = 6 \cr & \Rightarrow \frac{{6y}}{{10}} = \frac{{28}}{{10}} \cr & \Rightarrow y = \frac{{28}}{6} = 4.66 \cr} $$
∴ Average profit per sales rupee in women's shirt
$$\eqalign{ & = 4.66\% {\text{ of Rs}}.1 \cr & = {\text{Rs}}.\left( {\frac{{4.66}}{{100}}} \right) \cr & = {\text{Rs}}{\text{. }}0.0466 \cr} $$
91. A trader bought two horses for Rs. 19500, he sold one at a loss 20% and the other at a profit of 15%. If the selling price of each horse is the same, then their cost prices are respectively ?
a) Rs. 10000 and Rs. 9500
b) Rs. 11500 and Rs. 8000
c) Rs. 12000 and Rs. 7500
d) Rs. 10500 and Rs. 9000
Explanation: Let the CP of horse = Rs. x
Then, CP of second horse = Rs. (19500 - x)
According to the question,
$$\eqalign{ & x \times \frac{{80}}{{100}} = \left( {19500 - x} \right) \times \frac{{115}}{{100}} \cr & \Rightarrow 16x = 23\left( {19500 - x} \right) \cr & \Rightarrow 16x = 448500 - 23x \cr & \Rightarrow 39x = 448500 \cr & \Rightarrow x = \frac{{448500}}{{39}} \cr & \Rightarrow x = {\text{Rs}}{\text{.}}\,11500 \cr} $$
∴ CP of first horse = Rs. 11500
∴ CP of second horse
= Rs. 19500 - 11500
= Rs. 8000
92. A man sells two articles at Rs. 99 each. He gains 10% on one and loses 10% on the other. Then on overall basis he
a) Gains Rs. 2
b) Neither gains nor loses
c) Loses Rs. 2
d) Loses Rs. 1
Explanation:
$$\eqalign{ & {\text{Total Selling Price}} \cr & = {\text{Rs}}{\text{.}}\left( {2 \times 99} \right) \cr & = {\text{Rs}}.198 \cr & {\text{C}}{\text{.P}}{\text{. of first article}} \cr & = {\text{Rs}}.\left( {\frac{{100}}{{110}} \times 99} \right) \cr & = {\text{Rs}}{\text{. }}90 \cr & {\text{C}}{\text{.P}}{\text{. of second article}} \cr & = {\text{Rs}}.\left( {\frac{{100}}{{90}} \times 99} \right) \cr & = {\text{Rs}}{\text{. }}110 \cr & {\text{Total C}}{\text{.P}}{\text{.}} \cr & = {\text{Rs}}.\left( {90 + 110} \right) \cr & = {\text{Rs}}{\text{. }}200 \cr & \therefore {\text{Loss}} = {\text{Rs}}.\left( {200 - 198} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}2 \cr} $$
93.A man sold two steel chairs for Rs. 500 each. On one, he gains 20% and on the other, he loses 12%. How much does he gain or lose in the whole transaction ?
a) 1.5% gain
b) 1.5% loss
c) 2% gain
d) 2% loss
Explanation:
$$\eqalign{ & {\text{Total Selling Price}} \cr & = {\text{Rs}}.\left( {2 \times 500} \right) \cr & = {\text{Rs}}{\text{. }}1000 \cr & {\text{C}}{\text{.P}}{\text{. of first chair}} \cr & = {\text{Rs}}.\left( {\frac{{100}}{{120}} \times 500} \right) \cr & = {\text{Rs}}{\text{.}}\frac{{1250}}{3} \cr & {\text{C}}{\text{.P}}{\text{. of Second chair}} \cr & = {\text{Rs}}.\left( {\frac{{100}}{{88}} \times 500} \right) \cr & = {\text{Rs}}.\frac{{6250}}{{11}} \cr & {\text{Total C}}{\text{.P}}{\text{.}} \cr & = {\text{Rs}}.\left( {\frac{{1250}}{3} + \frac{{6250}}{{11}}} \right) \cr & = {\text{Rs}}.\left( {\frac{{32500}}{{33}}} \right) \cr & {\text{Gain}} = {\text{Rs}}.\left( {1000 - \frac{{32500}}{{33}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\left( {\frac{{500}}{{33}}} \right) \cr & \therefore {\text{Gain }}\% \cr & = \left( {\frac{{500}}{{33}} \times \frac{{33}}{{32500}} \times 100} \right)\% \cr & = 1.54\% \approx 1.5\% \cr} $$
94. Ranjan purchased 120 tables at a price of Rs. 110 per table. He sold 30 tables at a profit of Rs. 12 per table and 75 tables at a profit of Rs. 14 per table. The remaining tables were sold at a loss of Rs. 7 per table. What is the average profit per table ?
a) Rs. 10.04
b) Rs. 10.875
c) Rs. 12.80
d) Rs. 12.875
Explanation: Total C.P. = Rs. (120 × 110) = Rs. 13200
Total S.P.
= Rs. [(30 × 110 + 30 × 12) + (75 × 110 + 75 × 14) + (15 × 110 - 15 × 7)]
= Rs. 14505
$$\eqalign{ & {\text{Average profit }} \cr & {\text{ = Rs}}{\text{.}}\left( {\frac{{14505 - 13200}}{{120}}} \right) \cr & = {\text{Rs}}.\frac{{1305}}{{120}} \cr & = {\text{Rs}}.10.875 \cr} $$
95. x sells two articles for Rs. 4000 each with no loss and no gain in the transaction. If one was sold at a gain of 25% the other is sold at a loss of = ?
a) 25%
b) $$18\frac{2}{9}$$%
c) $$16\frac{2}{3}$$%
d) 20%
Explanation: Total SP = Rs. 8000 and Total CP = Rs. 8000
SP of 1st articles = Rs. 4000
Gain on it = 25%
∴ CP of 1st articles $$ = {\text{Rs}}{\text{.}}\,\left( {\frac{{100}}{{125}} \times 4000} \right) = {\text{Rs}}{\text{.}}\,3200$$
∴ CP of 2nd articles = Rs. (8000 - 3200) = Rs. 4800
SP of 2nd articles = Rs. 4000
∴ Loss on 2nd articles
$$\eqalign{ & = \left( {\frac{{800}}{{4800}} \times 100} \right)\% \cr & = 16\frac{2}{3}\% \cr} $$
96. Joseph's salary is reduced by 10% . In order to have his salary back to his original amount, it must be raised by = ?
a) 12.5%
b) $$11\frac{1}{9}$$%
c) 10%
d) 11%
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{income}} = 100 \cr & {\text{Reduce}}\,{\text{income}} = 90 \cr & \% {\text{Required}} = \frac{{10}}{{90}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{100}}{9}\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 11\frac{1}{9}\% \cr} $$
97. A shopkeeper sells two watches for Rs. 308 each. On one he gets 12% profit and on the other 12% loss. His profit or loss in the entire transaction was
a) Neither profit, nor loss
b) $$1\frac{{11}}{{25}}$$ % loss
c) $$1\frac{{11}}{{25}}$$ % profit
d) $$3\frac{2}{{25}}$$ % loss
Explanation:
$$\eqalign{ & {\text{loss }}\% \cr & = {\left( {\frac{{{\text{Common Loss and Gain}}\% }}{{10}}} \right)^2}\% \cr & = {\left( {\frac{{12}}{{10}}} \right)^2}\% \cr & = \frac{{36}}{{25}}\% \cr & = {\text{1}}\frac{{11}}{{25}}\% \cr & = {\text{1}}\frac{{11}}{{25}}\% {\text{ loss}}{\text{}} \cr} $$
98. A man sells two flats at the rate of Rs. 1.995 lakhs each. On one he gains 5% and on the other, he loses 5% . His gain or loss percent in the whole transaction is
a) 0.25% loss
b) 0.25% gain
c) 2.5% loss
d) 25% loss
Explanation:
$$\eqalign{ & {\text{Loss }}\% = {\left( {\frac{5}{{10}}} \right)^2}\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\left( {0.5} \right)^2}\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 0.25\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{0}}{\text{.25}}\% {\text{ loss}} \cr} $$
99. The list price of an article is Rs. 900. It is available at two successive discounts of 20% and 10% . The selling price of the article is = ?
a) Rs. 640
b) Rs. 648
c) Rs. 548
d) Rs. 548
Explanation:
$$\eqalign{ & 20\% = \frac{1}{5},\,\,10\% = \frac{1}{{10}} \cr & {\text{MP}}\,\,\,\,\,\,{\text{SP}} \cr & \,\,\,{\text{5}}\,\,\,\,\,\,\,\,\,\,\,{\text{4}} \cr & \frac{{10\,\,\,\,\,\,\,\,\,\,9}}{{50\,\,\,:\,\,\,36}} \cr & 50{\text{ units}} = 900 \cr & {\text{36 units}} = \frac{{900}}{{50}} \times 36 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 648 \cr} $$
100. A dishonest grocer sells rice at a profit of 10% and uses weight which are 20% less than the marked weight. The total gain earned by him will be = ?
a) 37.5%
b) 32%
c) 30.5%
d) 35%
Explanation: According to the question,
Grocer use 20% less weight
= 1000 - 200
= 800 gm.
$$\eqalign{ & {\text{The profit }}\% \cr & = \frac{{200}}{{800}} \times 100 \cr & = 25\% \cr & {\text{Then total profit }} \cr & = 10 + 25 + \frac{{25 \times 10}}{{100}} \cr & = 37.5\% \cr} $$