1. A shopkeeper wishes to give 5% commission on the marked price of an article but also wants to earn a profit of 10%. If his cost price is Rs. 95, then marked price is:
a) Rs. 100
b) Rs. 110
c) Rs. 120
d) Rs. 130
Discussion
Explanation: C.P = Rs. 95.
Then S.P = 95 + 10% of 95 = Rs. 104.5
Let Marked Price(M.P) = X. He gives 5% commission on M.P.
S.P = X - 5% of X
S.P = 0.95X
104.5 = 0.95X
X = $$\frac{{104.5}}{{0.95}} = 100$$
M.P = Rs. 110
2. A merchant has announced 25% rebate on prices of ready-made garments at the time of sale. If a purchaser needs to have a rebate of Rs. 400, then how many shirts, each costing Rs. 320, should he purchase?
a) 10
b) 6
c) 7
d) 5
Discussion
Explanation: Discount on one shirt,
= 25% of 320 = $$\frac{{320 \times 25}}{{100}}$$ = Rs. 80
Hence, number of shirt he must buy to get a rebate of Rs. 400 = $$\frac{{400}}{{80}}$$ = 5
3. The marked price of a shirt and trousers are in the ratio 1:2. The shopkeeper gives 40% discount on the shirt. If the total discount in the set of the shirt and trousers is 30%, the discount offered on the trousers is:
a) 15%
b) 20%
c) 25%
d) 30%
Discussion
Explanation: Let the price of shirt and trouser be Rs. 100 and Rs. 200 respectively.
Then, price of set of shirt and trouser = Rs. 300.
After giving 30% discount on the set,
Selling Price = 300 - 30% of 300 = 210.
Total Discount on Set = 90.
And Discount on shirt is 20% alone,
S.P of shirt alone = 100 - 40% of 100 = 60.
Rs. 40 is the discount on shirt then Rs. 50 must be the discount on the trouser.
So, discount on trouser = $$\frac{{50 \times 100}}{{200}}$$ = 25%.
4. A trader sells goods to a customer at a profit of k% over the cost price, besides it he cheats his customer by giving 880 g only instead of 1 kg. Thus his overall profit percentage is 255. Find the value of k?
a) 8.33%
b) 12.5%
c) 8.25%
d) 10%
Discussion
Explanation: % Profit = $$\frac{{25}}{{100}}$$ = $$\frac{{120 + {\text{k}}}}{{880}}$$
k = 100
Net % profit = $$\frac{{100 \times 100}}{{1000}}$$ = 10%
5. A man buys a chair and table for Rs. 6000. He sells the chair at a loss of 10% and the table at gain of 10%. He still gains Rs. 100 on the whole. Cost price of chair is:
a) Rs. 2500
b) Rs. 2850
c) Rs. 3050
d) Rs. 3500
Discussion
Explanation: If the C.P of the chair be Rs. x,
Total S.P = $$\frac{{{\text{x}} \times 90}}{{100}}$$ + $$\left( {\left( {6000 - {\text{x}}} \right) \times \frac{{110}}{{100}}} \right)$$
9x + 66000 - 11x = 61000
2x = 66000 - 61000 = 5000
x = Rs. 2500
6. By selling an article, a man makes a profit of 25% of its selling price. His profit percent is:
a) 20%
b) 25%
c) $$16\frac{2}{3}$$%
d) $$33\frac{1}{3}$$%
Discussion
Explanation: He gets 25% profit on the selling price.
$$\eqalign{ & Let\,S.P = x;\,then \cr & C.P = x - {\frac{x}{4}} \cr & = Rs.\,\frac{{3x}}{4} \cr & Hence, \cr & \% \,gain = {\frac{{ {\frac{x}{4}} }}{{ {\frac{{3x}}{4}} }}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{100}}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 33\frac{1}{3} \cr} $$
7. A trader sells his goods at a discount 20%. He still makes a profit of 25%. If he sells the goods at the marked price only, his profit will be:
a) 25.56%
b) 56.25%
c) 50.25%
d) 54.25%
Discussion
Explanation: Let the marked price = Rs. 100
Then, S.P = 100 - 20% of 100 = Rs. 80
Profit = 25%
Let C.P = X
S.P = 80
X + 25% of X = 80
Hence, X = Rs. $$\frac{{100 \times 80}}{{125}}$$ = Rs. 64
C.P = Rs. 64
Profit after selling on marked price = 100 - 64 = Rs. 36
% gain = $$\frac{{36 \times 100}}{{64}}$$ = 56.25%
8. A sells an article to B at gain of 25% B sells it to C at a gain of 20% and C sells it to D at a gain 10%. If D pays Rs. 330 for it, how much did it cost to A?
a) Rs. 200
b) Rs. 250
c) Rs. 275
d) Rs. 290
Discussion
Explanation: Let Cost Price for A was 100
Then C.P for B = 100 + 25% of 100 = 125
C.P for C = 125 + 20% of 125 = 150
C.P for D = 150 + 10% of 150 = 165
But, D pay Rs. 330, Then it must be equal to
165 = 330
1 = $$\frac{{330}}{{165}}$$
100 = $$\frac{{330 \times 100}}{{165}} = 200$$
Thus, C.P for A = Rs. 200
9. A dealer buys an article marked at Rs. 25,000 with 20% and 5% off. He spends Rs. 1,000 for its repairs and sells it for Rs. 25,000. What is his gain or loss percent?
a) loss of 25%
b) gain of 25%
c) gain 10%
d) loss of 10%
Discussion
Explanation: Marked Price = 25000.
After first discount it become,
= 25000 - 20% of 25000 = 20000.
After second discount, it becomes
= 20000 - 5% of 20000 = 19000.
So, S.P = 19000.
C.P for the man who bought it, as he spends 1000 on repair.
= 19000 + 1000 = 20000
Profit = 25000 - 20000 = 5000.
%Profit = $$\frac{{5000 \times 100}}{{20000}}$$ = 25%
10. By selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be:
a) Rs. 2600
b) Rs. 2700
c) Rs. 2800
d) Rs. 3000
Discussion
Explanation: C.P of bicycle = $$100 \times \frac{{2850}}{{114}}$$ = Rs. 2500
S.P for the profit of 8% = $$108 \times \frac{{2500}}{{100}}$$ = Rs. 2700
11. A shopkeeper calculate percentage profit on the buying price and another on the selling price. What will be their difference in profits if both claim a profit of 20% on goods sold for Rs. 3000?
a) Rs. 200
b) Rs. 100
c) Rs. 150
d) Rs. 400
Discussion
Explanation: For 20% profit on selling price means $$\frac{1}{5}$$ of 3000 i.e. Rs. 600
Now, let the C.P = Rs. 100, Then,
S.P with 20% profit = Rs. 120
For 20% profit on selling price means cost is 100 + profit is 20 = selling price is 120.
Means selling price is 120% of cost price.
Now selling price is 120% ie 3000 then find 100% amount which will be cost.
Cost = $$\frac{{3000}}{{120}}\% $$
= $$\frac{{3000}}{{\frac{6}{5}}}$$
Because, 120% = $$\frac{6}{5}$$
= 3000 x $$\frac{5}{6}$$
= 2500
Cost is 2500
Thus profit is 20% i.e. $$\frac{1}{5}$$ x 2500 = 500
Difference is 600 - 500 = Rs.100
12. A dishonest dealer marks up the price of his goods by 20% and gives a discount of 10% to the customer. Besides, he also cheats both his supplier and his buyer by 100 grams while buying or selling 1 kilogram. Find the percentage profit earned by the shopkeeper?
a) 20%
b) 25%
c) 32%
d) 50%
Discussion
Explanation:
While buying,
He buys 1100 gram instead of 1000 gram.
Suppose he bought 1100 grams for Rs. 1000.
While selling,
He sells only 900 grams when he takes the money for 1 kg.
Now, according to the problem,
he sells at a 8% profit (20% markup, 10% discount).
Hence, his selling price is Rs. 1080 for 900 grams.
1100 grams for Rs. 1000
Hence, 1188 grams for Rs. 1080
Selling: 900 grams for Rs. 1080
Hence, % profit = $$\frac{{288}}{{900}}$$ × 100 = 32%
(using goods left by goods sold formula)
13. A tradesman marks his goods at 25% above the cost price and allows purchasers a discount of $$\frac{{25}}{2}$$%, his profit is:
a) 8%
b) 8.5%
c) 8.625%
d) 9.375%
Discussion
Explanation:
Let C.P = Rs. 100
Marked Price(M.P) = 100 + 25% of 100 = 125
Now, discount = $$\frac{{25}}{2}$$% on M.P
So, S.P = 125 - $$\frac{{25}}{2}$$% of 125 = Rs. 109.375
%Gain = 9.375%
14. Profit on selling 10 candles equals selling price of 3 bulbs. While loss on selling 10 bulbs equal selling price of 4 candles. Also profit percentage equals to the loss percentage and cost of a candle is half of the cost of a bulb. What is the ratio of selling price of candles to the selling price of a bulb?
a) 5 : 4
b) 3 : 2
c) 4 : 5
d) 3 : 4
Discussion
Explanation: Candle - - - - - - - - Bulb
CP . . . . A - - - - - - - - B
SP . . . . C - - - - - - - - D
$$\eqalign{ & and.\,C = 2A \cr & {\text{Profit}} = 10\left( {B - A} \right) = 3D \cr & {\text{Loss}} = 10\left( {C - D} \right) = 4B \cr & {\text{Profit}}\% = \frac{{ {3D \times 100} }}{{10A}} \cr & {\text{Loss}}\% = \frac{{ {4B \times 100} }}{{10C}} \cr & \frac{{ {3D \times 100} }}{{10A}} = \frac{{ {4B \times 100} }}{{10C}} \cr & \frac{B}{D} = \frac{3}{2} = 3:2 \cr} $$
15. Find the selling price of goods if two salesmen claim to make 25% profit each, one calculating it on cost price while another on the selling price, the difference in the profits earned being Rs. 100 and selling price being the same in both the cases?
a) Rs. 1200
b) Rs. 1600
c) Rs. 2400
d) Rs. 2500
Discussion
Explanation: Let C.P's be Rs. 1000 each, their respective S.P will be,
1000 == 25%↑ ⇒ 1250 [person calculating profit on the C.P]
1000 == 33.33%↑ ⇒ 1333.33 [The person calculating his profit on S.P: 25% of S.P = 33.33% of C.P]
The difference turned out to be = 83.33. This has occured when we have assumed the C.P as 1000. But, we are given difference of Rs. 100
So, on comparing,
83.33 = 1000
1 = $$\frac{{1000}}{{83.33}}$$
100 = $$\frac{{1000}}{{83.33}} \times 100$$ = Rs. 1200
16. Cost price of 12 oranges is equal to the selling price of 9 oranges and the discount on 10 oranges is equal to the profit on 5 oranges. What is the percentage point difference between the profit percentage and discount percentage?
a) 20
b) 22.22
c) 16.66
d) 15
Discussion
Explanation: 12 C.P = 9 S.P,
So profit % = $$\frac{{12\,{\text{C}}{\text{.P}}{\text{.}} - 9\,{\text{C}}{\text{.P}}{\text{.}}}}{{9\,{\text{C}}{\text{.P}}{\text{.}}}}$$ = 33.33.
Then it is said that,
5 S.P - 5 C.P = 10 M.P -10 S.P
From that we get relation between M.P and S.P, that is,
27 S.P = 24 M.P(With help of 12 C.P = 9 S.P)
Then Discount % = $$\frac{{{\text{M.P}} - {\text{S.P}}}}{{{\text{M.P}}}}$$ = 11.11%
So, % point discount = 33.33% - 11.11% = 22.22%
17. A retailer increase the selling price by 25% due to which his profit percentage increase from 20% to 25%. What is the percentage increase in cost price ?
a) 20%
b) 30%
c) 25%
d) 50%
Discussion
Explanation: 100 (Initial C.P) -- 20%↑ (initial profit) → 120(S.P)
120 (S.P) -- 25%↑ → 150 (New S.P)
Let x be the new Cost price
Selling Price = 150
x × 1.25 = 150
x = 120
% change = $$ {\frac{{120 - 100}}{{100}}} \times 100$$ = 20%
18. Two successive price increase of 10% and 10% of an article are equivalent to a single price increase of:
a) $$26\frac{2}{3}$$
b) 25%
c) 21%
d) $$33\frac{1}{3}$$
Discussion
Explanation: 100 --- 10%↑ → 110 --- 10%↑ → 121
Equivalent price increase = 21%
19. A tradesman fixed his selling price of goods at 30% above the cost price. He sells half the stock at this price, one-quarter of his stock at a discount of 15% on the original selling price and rest at a discount of 30% on the original selling price. Find the gain percentage altogether?
a) 14.875%
b) 15.375%
c) 15.575%
d) 16.375%
Discussion
Explanation: Let C.P = 100; then marked price = 130;
Now, revenue
$$ = { {\frac{1}{2}} \times 130 + {\frac{1}{4}} \times 0.85 \times 130 + {\frac{1}{4}} \times 0.7 \times 130} $$
$$\eqalign{ & = 65 + 27.65 + 22.5 \cr & = 115.4 \cr & \% {\text{profit}} = \frac{{15.4 \times 100}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15.4\% \cr} $$
20. A bicycle marked at Rs. 2,000, is sold with two successive discount of 20% and 10%.An additional discount of 5% is offered for cash payment. The selling price of the bicycle at cash payment is:
a) Rs. 1,568
b) Rs. 1,368
c) Rs. 1,468
d) Rs. 1,668
Discussion
Explanation: Marked Price = 2000
S.P after first Discount of 20% = 2000 - 20% of 2000 = 1600
S.P after second Discount of 10% = 1600 - 10% of 1600 = 1440
Now, the final selling price at cash = 1440 - 5% of 1440 = Rs. 1368
21. A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
a) No profit, no loss
b) 5%
c) 8%
d) 10%
Discussion
Explanation:
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{. of 56 kg rice}} \cr & = {\text{ }}Rs.{\text{ }}\left( {26{\text{ }} \times {\text{ }}20{\text{ }} + {\text{ }}30{\text{ }} \times {\text{ }}36} \right) \cr & = {\text{ }}Rs.{\text{ }}\left( {520{\text{ }} + {\text{ }}1080} \right) \cr & = {\text{ }}Rs.{\text{ }}1600 \cr & {\text{S}}{\text{.P}}{\text{. of 56 kg rice}} \cr & = {\text{ }}Rs.{\text{ }}\left( {56{\text{ }} \times {\text{ }}30} \right) \cr & = {\text{ }}Rs.{\text{ }}1680 \cr & \therefore {\text{Gain}} = \left( {\frac{{80}}{{1600}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5\% \cr} $$
22. The ratio of the cost price and selling price is 5 : 4, the loss percent is = ?
a) 20%
b) 25%
c) 40%
d) 50%
Discussion
Explanation:
$$\eqalign{ & \frac{{{\text{Cost price}}}}{{{\text{Selling price}}}} = \left. {\frac{5}{4}} \right\}{\text{1 unit loss}} \cr & {\text{loss}}\% = \frac{1}{5} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 20\% {\text{ loss}} \cr} $$
23. If selling price of an article is $$\frac{8}{5}$$ times of its cost price, the profit percent on it is
a) 120%
b) 160%
c) 40%
d) 60%
Discussion
Explanation:
$$\eqalign{ & {\text{Selling price}} \cr & = \frac{8}{5} \times {\text{Cost price}} \cr & \frac{{{\text{Selling price}}}}{{{\text{Cost price}}}} = \left. {\frac{8}{5}} \right\}{\text{3 gain}} \cr & {\text{Gain}}\% = \frac{3}{5} \times 100 = 60\% {\text{ }} \cr} $$
24. If the cost price of 12 oranges is equal to selling price of 10 oranges, then the percentage of profit is =?
a) 16%
b) 20%
c) 18%
d) 25%
Discussion
Explanation:
12 Cost Price = 10 Selling Price
$$\eqalign{ & \frac{{{\text{CP}}}}{{{\text{SP}}}} = \frac{{10}}{{12}} = \left. {\frac{5}{6}} \right\}{\text{1 profit}} \cr & {\text{Profit }}\% = \frac{1}{5} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 20\% \cr} $$
25. The cost price of an article is Rs. 7840. What should be the selling price of the article so that there is a profit of 7% ?
a) Rs. 8000
b) Rs. 8300
c) Rs. 8388.80
d) Rs. 8500
Discussion
Explanation:
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}.7840 \cr & {\text{Profit}} = 7\% \cr & \therefore {\text{S}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {\frac{{107}}{{100}} \times 7840} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}8388.80 \cr} $$
26. Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:
a) 30%
b) $$33\frac{1}{3}$$
c) 35%
d) 44%
Discussion
Explanation:
$$\eqalign{ & {\text{Suppose,}}\,{\text{no.}}\,{\text{of}}\,{\text{articles}}\,{\text{bought}} \cr & {\text{ = }}\,{\text{L}}{\text{.C}}{\text{.M}}{\text{.}}\,{\text{of}}\,{\text{6}}\,{\text{and}}\,{\text{5 = 30}} \cr & {\text{C}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{30}}\,{\text{articles}} \cr & = Rs.\,\left( {\frac{5}{6} \times 30} \right) = Rs.\,25 \cr & {\text{S}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{30}}\,{\text{articles}} \cr & = Rs.\,\left( {\frac{6}{5} \times 30} \right) = Rs.\,36 \cr & \therefore {\text{Gain}}\,\% = \left( {\frac{{11}}{{25}} \times 100} \right)\% \, = 44\% \cr} $$
27. 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) 45
b) 50
c) 55
d) 60
Discussion
Explanation:
$$\eqalign{ & {\text{(C}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{17}}\,{\text{balls) - (S}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{17}}\,{\text{balls) = (C}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{5}}\,{\text{balls)}} \cr & \Rightarrow {\text{C}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{12}}\,{\text{balls = S}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{17}}\,{\text{balls = Rs}}{\text{.720}} \cr & \Rightarrow {\text{C}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{1}}\,{\text{ball}} = Rs.\,\left( {\frac{{720}}{{12}}} \right) = Rs.\,60 \cr} $$
28. When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?
a) Rs. 21,000
b) Rs. 22,500
c) Rs. 25,300
d) Rs. 25,800
Discussion
Explanation:
$$\eqalign{ & 85:18700 = 115:x \cr & \Rightarrow x = {\frac{{18700 \times 115}}{{85}}} = 25300 \cr & {\text{Hence,}}\,{\text{S}}{\text{.P}}{\text{.}} = Rs.\,25300 \cr} $$
29. 100 oranges are bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen. The percentage of profit or loss is:
a) $$14\frac{2}{7}$$% gain
b) 15% gain
c) $$14\frac{2}{7}$$% loss
d) 15% loss
Discussion
Explanation:
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{1}}\,{\text{orange}}\, \cr & = Rs.\,\left( {\frac{{350}}{{100}}} \right) = Rs.\,3.50 \cr & {\text{S}}{\text{.P}}{\text{.}}\,{\text{of}}\,{\text{1}}\,{\text{orange}} \cr & = Rs.\,\left( {\frac{{48}}{{12}}} \right) = Rs.\,4 \cr & \therefore {\text{Gain}}\% = \left( {\frac{{0.50}}{{3.50}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{100}}{7}\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 14\frac{2}{7}\% \cr} $$
30. A shopkeeper sells one transistor for Rs. 840 at a gain of 20% and another for Rs. 960 at a loss of 4%. His total gain or loss percent is:
a) $$5\frac{{15}}{{17}}$$% loss
b) $$5\frac{{15}}{{17}}$$% gain
c) $$6\frac{2}{3}$$% gain
d) None of these
Discussion
Explanation:
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{.}}\,{\text{of}}\,{1^{st}}\,{\text{transistor}} \cr & = Rs.\,\left( {\frac{{100}}{{120}} \times 840} \right) = Rs.\,700 \cr & {\text{C}}{\text{.P}}{\text{.}}\,{\text{of}}\,{2^{nd}}\,{\text{transistor}} \cr & = Rs.\,\left( {\frac{{100}}{{96}} \times 960} \right) = Rs.\,1000 \cr & {\text{So,}}\,{\text{total}}\,{\text{C}}{\text{.P}}{\text{.}}\, = Rs.\,\left( {700 + 1000} \right) = Rs.\,1700 \cr & {\text{Total}}\,{\text{S}}{\text{.P}}{\text{.}}\, = \,Rs.\,\left( {840 + 960} \right) = Rs.\,1800 \cr & \therefore {\text{Gain}}\,\% = \left( {\frac{{100}}{{1700}} \times 100} \right)\% = 5\frac{{15}}{{17}}\% \cr} $$
31. A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent ?
a) $$4\frac{1}{6}$$%
b) $$6\frac{1}{4}$$%
c) $$8\frac{1}{3}$$%
d) 20%
Discussion
Explanation:
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{. of 1 kg}} \cr & = {\text{Rs}}.\left( {\frac{{420}}{{70}}} \right) \cr & = {\text{Rs}}{\text{. }}6. \cr & {\text{S}}{\text{.P}}{\text{. of 1 kg}} \cr & = {\text{Rs}}{\text{. }}6.50. \cr & {\text{Gain}}\% = \left( {\frac{{0.50}}{6} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{25}}{3}\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 8\frac{1}{3}\% \cr} $$
32. A merchant marked cloth at Rs. 50 metre. He offers 2 successive discounts of 15% and 20%. The net price/metre is =?
a) Rs. 32.50
b) Rs. 42.50
c) Rs. 34.00
d) Rs. 40.00
Discussion
Explanation:
$$\eqalign{ & 15\% = \frac{3}{{20}}\left( - \right) \cr & 20\% = \frac{1}{5}\left( - \right) \cr} $$
| Marked Price | : | Net Price |
| 20 | : | 17 |
| 5 | : | 4 |
| 100 | : | 68 |
1 unit = Rs. 0.50
68 units = Rs. 34
33. If the cost price of 10 articles is equal to the selling price of 7 articles, then the gain or loss percent is = ?
a) 51% gain
b) $$42\frac{6}{7}$$% gain
c) 35% loss
d) $$42\frac{6}{7}$$% loss
Discussion
Explanation:
10 Cost Price = 7 Selling Price
$$\eqalign{ & \frac{{{\text{CP}}}}{{{\text{SP}}}} = \left. {\frac{7}{{10}}} \right\rangle {\text{3 unit profit}} \cr & {\text{Profit}}\% = \frac{3}{7} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 42\frac{6}{7}\% {\text{ gain}} \cr} $$
34. A coconut merchant finds that the cost price of 2750 coconuts is the same as the selling price of 2500 coconuts. His loss or gain will be =?
a) 5% loss
b) 10% gain
c) 15% loss
d) 20% gain
Discussion
Explanation:
2750 Cost Price = 2500 Selling Price
$$\eqalign{ & \frac{{{\text{CP}}}}{{{\text{SP}}}} = \frac{{2500}}{{2750}} = \left. {\frac{{10}}{{11}}} \right\rangle {\text{1 unit profit}} \cr & {\text{Profit}}\% = \frac{1}{{10}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10\% {\text{ gain}} \cr} $$
35. By selling an article for Rs. 100 a man gains Rs.15. Then, his gain % is -
a) 15%
b) $$12\frac{2}{3}$$%
c) $$17\frac{{11}}{{17}}$$%
d) $$17\frac{1}{4}$$%
Discussion
Explanation:
$$\eqalign{ & {\text{S}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. }}100 \cr & {\text{Gain}} = {\text{Rs}}{\text{. }}15. \cr & {\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {100 - 15} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}85 \cr & {\text{Gain }}\% = \left( {\frac{{15}}{{85}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{300}}{{17}}\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 17\frac{{11}}{{17}}\% \cr} $$
36. A trader buys some goods for Rs. 150. If the overhead expenses be 12% of cost price, then at what price should it be sold to earn 10% ?
a) Rs. 184.80
b) Rs. 185.80
c) Rs. 187.80
d) Rs. 188.80
Discussion
Explanation:
Total C.P. = Cost + Overhead Expenses
= Rs. (150 + 12% of 150)
= Rs. (150 + 18)
= Rs. 168
$$\eqalign{ & {\text{S}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {\frac{{110}}{{100}} \times 168} \right) \cr & = {\text{Rs}}{\text{. }}184.80 \cr} $$
37. If the loss of percent on article is 15%. Then the ratio of the cost price and selling price will be = ?
a) 17 : 20
b) 20 : 17
c) 23 : 15
d) 15 : 23
Discussion
Explanation:
The loss of percent on article is 15%
$$\eqalign{ & 15\% = \frac{{15}}{{100}} = \frac{{3 \to {\text{Loss}}}}{{20 \to {\text{C}}{\text{.P}}{\text{.}}}} \cr & {\text{Selling price }} = 17 \cr & {\text{C}}{\text{.P}}{\text{.}}:{\text{S}}{\text{.P}}{\text{.}} = 20:17 \cr} $$
38. List price of T.V is Rs. 2300 and discount series found to be 25% ans 10%. Then the selling price of T.V is = ?
a) Rs. 1255.50
b) Rs. 1525.50
c) Rs. 1552.50
d) Rs. 1555.20
Discussion
Explanation:
$$\eqalign{ & {\text{List price of T}}{\text{.V}} = {\text{2300}} \cr & {\text{Selling price}} \cr & = 2300 \times \frac{{75}}{{100}} \times \frac{{90}}{{100}} \cr & = {\text{Rs}}{\text{. 1552}}{\text{.50}} \cr} $$
39. Gopi goes from place A to B to bye an article costing 15% less at B, although he spends Rs. 150 on travelling, still he gains Rs. 150 compared to buying it at A. His profit percent is = ?
a) 4.5%
b) 6%
c) 7.5%
d) 8%
Discussion
Explanation:
Let price at A = 100x
Then price at B = 85x → 15%
Discount
According to the question,
100x - (85x + 150) = 150
15x = 300
x = 20
Price at A = 100 × 20 = 2000
Price at B including travelling charges
= 85x = 150
= 85 × 20 + 150
= 1700 + 150
= 1850
$$\eqalign{ & {\text{Percentage profit }} \cr & = \frac{{2000 - 1850}}{{2000}} \times 100 \cr & = \frac{{150}}{{2000}} \times 100 \cr & = 7.5\% \cr} $$
40. If an article is sold at 200 percent profit, then the ratio of its cost price to its selling price will be -
a) 1 : 2
b) 2 : 1
c) 1 : 3
d) 3 : 1
Discussion
Explanation:
Let C.P. = Rs. x
Profit = 200%
S.P. = 300% of Rs. x = Rs. 3x
Required ratio = x : 3x = 1 : 3
41. A style cloth emporium the shopkeeper measures 20% less for every metre of cloth also he marks-up goods by 20%. What is the profit percentage?
a) 50%
b) 65%
c) 75%
d) 85%
Discussion
Explanation: Let CP = Rs. 100, then SP will be 120.
He gives cloth worth Rs. 80 instead of Rs. 100.
% Profit = $$ {\frac{{120 - 80}}{{80}}} \times 100 = 50\% $$
42. A traders sells two acrticles, one at a loss of 10% and another at a profit of 15% but finally there is no loss or gain. If the total sale price of these two articles is Rs. 30,000, find the difference between their cost prices:
a) Rs. 5000
b) Rs. 6000
c) Rs. 7500
d) Rs. 8500
Discussion
Explanation:10% of x = 15 % of y, where x + y = 30000
$$\frac{{\text{x}}}{{\text{y}}} = \frac{{3{\text{k}}}}{{2{\text{k}}}}$$
Hence, difference = k = Rs. 6000
43. The difference between a discount 40% on Rs. 500 and two successive discounts of 30% and 10% the same amount is
a) Rs. 20
b) Rs. 10
c) Rs. 15
d) Rs. 0
Discussion
Explanation: 40% discount on 500 = $$\frac{{40 \times 500}}{{100}}$$ = Rs. 200
Two successive discount 30% and 10% on 500 would be
500 ===30% discount ⇒ Rs. 350
350 ===10% discount = 315
Total discount in first case = Rs. 200
Total discount in second case = 500 - 315 = Rs. 185
difference = Rs. 15
44. A person having bought goods for Rs. 400 sells half of it at a gain of 5%, at what gain % must he sell the remainder so as to gain 20% on the whole?
a) 30%
b) 32%
c) 34%
d) 35%
Discussion
Explanation: To gain 20% on whole he must sell all good for,
Rs. 400 + 20% of 400 = 480
As he get 5% gain on half of the goods i.e.
200 + 5% of 200 = 210
So required balance = 480 - 210 = 270
He must gain Rs. 70 on rest Rs. 200
% gain on remainder goods = $$\frac{{70 \times 100}}{{200}}$$ = 35%
45. Find the difference of amount if 40% discount is given on Rs. 500 and two consecutive discount 30% and 10% are given on the same amount.
a) Rs. 15
b) Rs. 0
c) Rs. 20
d) Rs. 10
Discussion
Explanation: 40% discount on 500 = $$\frac{{40 \times 500}}{{100}}$$ = Rs. 200
Two successive discount on 500,
= 30% of 500 + 10% of (500 - 30% of 500)
= 150 + 10% of 350
= 150 + 35 = Rs. 185
Difference in Discount = 200 - 185 = Rs. 15
46. A man purchased the articles for Rs. 123684. He sold 60% of those at a profit of 16.66% and rest at a loss. Find the loss percentage on the remaining if the overall loss is 14%?
a) 20%
b) 30%
c) 60%
d) 66.66%
Discussion
Explanation: He gets 14% of loss that means he gets 86% of CP.
Let CP be Rs. 100
60% of 100 + 16.66% of 60% of 100 + 40% of 100 - x% of 40% of 100 = 86% of 100
70 + 40X = 86
40X = 86 - 70 = 16
X = $$\frac{{16}}{{40}}$$
X = 0.4
Loss = 1 - 0.4 = 0.6 = 60%
47. A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for Rs. 240. What is original price per kg of sugar
a) Rs. 10 per Kg
b) Rs. 8 per Kg
c) Rs. 6 per Kg
d) Rs. 5 per Kg
Discussion
Explanation: Reduction in price 20% amount of sugar will increase 25%
It means,
25% = 6 Kg.
Initially, total Sugar = 6 × 4 = 24Kg.
Original price of the sugar was,
$$\frac{{240}}{{24}}$$ = Rs. 10 per kg.
48. A dishonest dealer purchases goods at 20% discount of the cost price of Rs. X and also cheats his wholesaler by getting 20% extra through false weighing, per kg. Then he marks up his goods by 80% of x, but he gives a discount of 25% besides he cheats his customer by weighing 10% less than the required. What is his overall profit percentage?
a) 125%
b) 100%
c) 98.66%
d) 120%
Discussion
Explanation: Let actual cost price of an article be Rs. 1 (in place of X). Now he purchases goods worth Rs. 120 and pays Rs. 80, since 20% discount is allowed.
CP = $$\frac{{80}}{{120}} = \frac{2}{3}$$
Again, MP, SP = 135 (since 25% discount)
Thus, the trader sells goods worth Rs. 90 instead of 100g and charges Rs. 135.
Then the effective SP = $$\frac{{135}}{{90}} = \frac{3}{2}$$
$$\eqalign{ & {\text{Profit}}\,\% \cr & = {\frac{{ { {\frac{3}{2}} - {\frac{2}{3}} } }}{{\frac{2}{3}}}} \times 100 \cr & = 125\% \cr} $$
49. Hotel Aditya has 10 single AC rooms, 5 double AC rooms and 18 non AC rooms. The fixed monthly rent of hotel is 150,000. The per day maintenance cost is Rs. 100 for double AC room, Rs. 75 for single AC room and Rs. 40 for non AC room. The per day charges are Rs. 600 for double AC room, Rs. 400 for single AC room and Rs. 250 for non AC room. In April 2003, the occupancy rate of non AC room was 50%, 70% of single AC room and 40% of double AC rooms. Find the profit/loss % for that particular month.
a) 10.33% (profit)
b) 10.33% (loss)
c) 5.67% (loss)
d) 5.67% (profit)
Discussion
Explanation: Maintenance,
= Rs. (100 × 5 × 30) + (75 × 10 × 30) + (40 × 18 × 30)
= 15,000 + 22,500 + 21,600
= Rs. 59,100
Total cost = 2,09,100
Amount Received,
= (9 × 250 × 30) + (7 × 400 × 30) + (2 × 600 × 30)
= 67,500 + 84,000 + 36,000
= 1, 87, 500
Loss (%)
$$\eqalign{ & = {\frac{{209100 - 187500}}{{209100}}} \times 100 \cr & = {\frac{{21600}}{{209100}}} \times 100 \cr & = 10.33\% \cr} $$
50. A bookseller procures 40 books for Rs. 3200 and sells them at a profit equal to the selling price of 8 books. What is the selling price of one dozen books, if the price of each book is same?
a) 720
b) 960
c) 1200
d) 1440
Discussion
Explanation: Cost price of each book,
= $$\frac{{3200}}{{40}}$$ = Rs. 80
Selling Price of 40 books = CP of 40 books + SP of 8 books
Selling Price of 40 books - SP of 8 books = CP of 40 books
SP of 32 books = Rs. 3200
SP of 1 book = $$\frac{{3200}}{{32}}$$ = Rs. 100
Selling price of one dozen (12) book = 12 × 100 = Rs. 1200
51. The marked price of an item is twice the cost price, discount 20% of market price and profit is 10% of selling price. Find profit percentage to cost
a) $$\frac{{100}}{9}$$%
b) $$\frac{{100}}{11}$$%
c) 11%
d) 85%
Discussion
Explanation:
MP = Rs. 200
Discount = 20%
Profit = Rs. 16
SP = 200 - 20% of 200 = 200 - 40 = Rs. 160
CP = SP - profit = 160 - 16 = Rs.144
% profit = $$\frac{{16 \times 100}}{{144}} = 11.11\% = \frac{{100}}{9}\% $$
52. The marked price of an item is twice the cost price. For a gain of 15%, the discount should be:
a) 7.5%
b) 20.5%
c) 32.5%
d) 42.5%
Discussion
Explanation: Let CP = Rs. 100
MP = Rs. 200
Gain = 15%
SP = 100 + 15% of 100 = Rs. 115
Discount = 200 - 115 = 85
% Discount = $$\frac{{85 \times 100}}{{200}}$$ = 42.5%
53. A man sold his watch at a loss of 5%. Had he sold it for Rs. 56.25 more, he would have gained 10%. What is the cost price of the watch (in Rs.)?
a) 365
b) 370
c) 375
d) 390
Discussion
Explanation: He sold his watch at loss of 5%. If he sells his watch for Rs. 56.25 more, he would gain 10%.
15% = Rs. 56.25.
1% = $$\frac{{56.25}}{{15}}$$
100% = $$\frac{{56.25 \times 100}}{{15}}$$ = Rs. 375
The cost price of the watch is Rs. 375
54. A total profit of Rs. 3,600 is to be distributed amongst A, B and C such that A : B = 5 : 4 and B : C = 8 : 9. The share of C in the profit is :
a) 1200
b) 1500
c) 1650
d) 1700
Discussion
Explanation: A Total Profit = Rs. 3600
Profit ratio,
A : B = 5 : 4
B : C = 8 : 9
As B is common in both ratio, we make B equal in both ratio by multiplying One B in another.
A : B = 5 : 4 × 8
B : C = 8 × 4 : 9
So, ratio of
A : B : C = 40 : 32 : 36 = 10 : 8 : 9
C shares in profit = $$\frac{{3600 \times 9}}{{27}}$$ = Rs. 1200
55. A man bought a horse and a cart. If he sold the horse at 10 % loss and the cart at 20 % gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. The amount paid by him was Rs._______ for the horse and Rs.________ for the cart.
a) 500, 300
b) 200, 400
c) 400, 200
d) 300, 500
Discussion
Explanation: Let X be the cost of horse and Y be the cost of the cart.
10% of loss in selling horse = 20% of gain in selling the cart.
$$\frac{{10}}{{100}} \times {\text{X}}$$ = (20 × 100) × Y
X = 2y --------------(1)
5% of loss in selling horse is 10 more than the 5% gain in selling the cart.
Therefore, $$\frac{5}{{100}} \times {\text{X}} - 10 = \frac{5}{{100}} \times {\text{Y}}$$
5X – 1000 = 5Y
Using equation (1),
10Y – 1000 = 5Y
5Y = 1000
Y =200
X = 400
CP of Horse = Rs. 400
CP of the Cart = Rs. 200
56. Abhishek purchased 140 shirts and 250 trousers @ Rs. 450 and @ Rs. 550 respectively. What should be the overall average selling price of shirts and trousers so that 40% profit is earned ? (rounded off to next integer)
a) Rs. 700
b) Rs. 710
c) Rs. 720
d) Rs. 725
Discussion
Explanation: Total Cost Price
= Rs. (140 × 450 + 250 × 550)
$$\eqalign{ & = {\text{Rs}}.\left( {63000 + 137500} \right) \cr & = {\text{Rs}}{\text{. }}200500. \cr & {\text{Total Selling Price}} \cr & = {\text{Rs}}.\left( {\frac{{140}}{{100}} \times 200500} \right) \cr & = {\text{Rs}}{\text{. }}280700. \cr & {\text{Average Selling Price}} \cr & = {\text{Rs}}.\left( {\frac{{280700}}{{140 + 250}}} \right) \cr & = {\text{Rs}}.\left( {\frac{{280700}}{{390}}} \right) \cr & = {\text{Rs}}{\text{. }}719.74 \approx 720 \cr} $$
57. A man sells two chairs at Rs. 120 each and by doing so he gains 25% on one chair and loses 25% on the other. His loss on the whole in Rs. is = ?
a) 20
b) 16
c) 25
d) 30
Discussion
Explanation:
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{.}}\,{\text{of first chair}} \cr & = \frac{{100}}{{125}} \times 120 = {\text{Rs}}{\text{.}}\,96 \cr & {\text{C}}{\text{.P}}{\text{.}}\,\,{\text{of}}\,{\text{second}}\,{\text{chair}} \cr & = \frac{{100}}{{75}} \times 120 = {\text{Rs}}{\text{.}}\,160 \cr & {\text{Loss}} = 160 + 96 - 240 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,16 \cr} $$ .
58. A man wanted to sell an article with 20% profit: but he actually sold at 20% loss for Rs. 480, at what price he wanted to sell it to earn the profit = ?
a) Rs. 720
b) Rs. 840
c) Rs. 600
d) Rs. 750
Discussion
Explanation:
$$\eqalign{ & {\text{Loss }}20\% \cr & {\text{Selling price}} \cr & = 100\% - 20 = 80\% \cr & 80\% = 480 \cr & 1 = \frac{{480}}{{80}} \cr & \left( {{\text{Profit }}20\% } \right) \cr & = \frac{{480}}{{80}} \times 120 \cr & = {\text{Rs}}{\text{. }}720 \cr} $$
59. A shopkeeper sells an article at a loss of $$12\frac{1}{2}$$% . Had he sold it for Rs. 51.80 more, he would have earned a profit of 6% . The cost price of the article is = ?
a) Rs. 280
b) Rs. 300
c) Rs. 380
d) Rs. 400
Discussion
Explanation: Let C.P. be Rs. x Then
(106% of x) - $$\left( {87\frac{1}{2}\% \,\,{\text{of}}\,x} \right) = 51.80$$
$$\eqalign{ & 18\frac{1}{2}\% \,\,{\text{of}}x = 51.80 \cr & x = \left( {\frac{{51.80 \times 100 \times 2}}{{37}}} \right) \cr & x = 280 \cr} $$
60. A person purchased 10 dozen pens at the rate of Rs. 4 per dozen. On checking, he found that 20 pens were not working. In order to earn 25% profit, he should sell the remaining pens each at -
a) 40 paise
b) 44 paise
c) 50 paise
d) 55 paise
Discussion
Explanation: Total C.P. of (10 × 12) i.e.,
120 pens = Rs. (4 × 10) = Rs. 40
No. of working pens
= (120 - 20) = 100
Total selling price of 100 pens
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {\frac{{125}}{{100}} \times 40} \right) \cr & = {\text{Rs}}{\text{. }}50 \cr & {\text{S}}{\text{.P}}{\text{.of each pen}} \cr & = {\text{Rs}}.\left( {\frac{{50}}{{100}}} \right) \cr & = {\text{50 paise}}{\text{}} \cr} $$
61. A grocer professes to sell goods at the cost price but uses false weights. He gains $$\frac{{100}}{9}$$% in this manner. He uses a weight of
a) 950gms
b) 900gms
c) 900gms
d) 940gms
Discussion
Explanation:
$$\eqalign{ & {\text{Gain}}\% \cr & = {\frac{{ {{\text{True}}\,{\text{Weight}} - {\text{False}}\,{\text{Weight}}} }}{{{\text{False}}\,{\text{Weight}}}}} \times 100 \cr & \frac{{100}}{9} = {\frac{{ {1 - x} }}{x}} \times 100 \cr & \frac{{ {1 - x} }}{x} = \frac{1}{9} \cr & 10x = 9 \cr & x = 0.9\,kg = 900\,gms \cr} $$
62. Find the difference of amount if 40% discount is given on Rs. 500 and two consecutive discounts 30% and 10% are given on the same amount
a) Rs. 15
b) Rs. 0
c) Rs. 20
d) Rs. 10
Discussion
Explanation: 40% discount on 500 = 200
Two consecutive discount on 500:
500 == 30% down ⇒ 350 == 10% down ⇒ 315 Total discount = 150 + 35 = 185
difference = 200 - 185 = Rs. 15
63. A trader marks his goods 40% above cost price and allows a discount of 25%. The profit he makes is:
a) 15%
b) 10%
c) 5%
d) 2%
Discussion
Explanation: Let original CP = Rs. 100
Then, the Marked Price = 40% of 100 + 100 = 140
SP = 140 - 25% of 140 = 105
%Profit = $$\frac{{5 \times 100}}{{100}} = 5\% $$
64. With a 5% discount on the cost of sugar a buyer could purchase 2 kg more sugar for Rs. 608. Selling Price of Sugar is:
a) Rs. 15.20
b) Rs. 15
c) Rs. 16.50
d) Rs. 2
Discussion
Explanation:
$$\eqalign{ & {\text{Let Initial Price of sugar was }}X. \cr & {\text{After Discount of }}5\% , \cr & {\text{the price of the sugar become}}, \cr & = X - 5\% \,of\,X \cr & = X - {\frac{{5X}}{{100}}} \cr & = \frac{{ {100X - 5X} }}{{100}} \cr & = \frac{{95X}}{{100}} \cr & {\text{Amount of sugar now,}} \cr & {\text{Buyer gets in }}Rs.608, \cr & = \frac{{608}}{{ {\frac{{95X}}{{100}}} }} \cr & = \frac{{ {608 \times 100} }}{{95}} \cr & {\text{Amount of sugar he gets - }} \cr & {\text{before the discount,}} \cr & = \frac{{608}}{X} \cr & \frac{{608}}{{ {\frac{{95X}}{{100}}} }} - \frac{{608}}{x} = 2 \cr & {\text{On}}\,{\text{Solving}} \cr & X = Rs.\,16 \cr & {\text{After discount price become}} \cr & = 16 - 5\% \,of\,16 \cr & = Rs.\,15.20 \cr} $$
65. A fruit seller buys some oranges and by selling 40% of them he realizes the cost price of all the oranges. As the oranges being to grow over-ripe, he reduces the price and sells 80% of the remaining oranges at half the previous rate of profit. The rest of the oranges being rotten are thrown away. The overall percentage of profit is:
a) 80
b) 84
c) 94
d) 96
Discussion
Explanation: Let fruit seller buys 100 oranges for Rs. 100
On selling of 40% of the oranges he realizes his cost price i.e. He sells 40 oranges for Rs. 100
Profit on 40 Oranges = 100 - 40 = Rs. 60
% profit on 40 oranges = $$\frac{{60 \times 100}}{{40}}$$ = 150%
Now, he sells 80% of 60 oranges on half of the previous profit i.e. 48 oranges, he sells at 75% of profit
SP of 48 oranges = 48 + 75% of 48 = 84
12 was rotten so he threw away.
Total SP = 100 + 84 = Rs. 184
Profit = 184 - 100 = 84
%Profit = 84%
66. Jacob bought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of Rs. 1100. How much did he spend on repairs if he made a profit of 20% ?
a) Rs. 400
b) Rs. 440
c) Rs. 500
d) Rs. 550
Discussion
Explanation:
$$\eqalign{ & {\text{Let the C.P. be Rs. }}x \cr & {\text{Then, }}20\% {\text{ of }}x = 1100 \cr & \Rightarrow \frac{{20}}{{100}} \times x = 1100 \cr & \Rightarrow x = 5500 \cr & {\text{C}}{\text{.P}}. = {\text{Rs}}{\text{. }}5500 \cr} $$
Expenditure on repairs = 10%
$$\eqalign{ & {\text{Actual price}} \cr & = {\text{Rs}}.\left( {\frac{{100}}{{110}} \times 5500} \right) \cr & = {\text{Rs}}{\text{. }}5000. \cr & {\text{Expenditure on repairs}} \cr & = {\text{Rs}}.\left( {5500 - 5000} \right) \cr & = {\text{Rs}}{\text{. }}500 \cr} $$
67. A person sells a table at a profit of 10% . If he had bought the table at 5% less cost and sold for Rs. 80 more, he would have gained 20% . The cost price of the table is = ?
a) Rs. 3200
b) Rs. 2500
c) Rs. 2000
d) Rs. 200
Discussion
Explanation: Let the CP1 of Table = 100x
Initial SP1 = 100x + 10% of 100x = 100x + 10x = 110x
If He brought table at 5% discount. Therefore CP2 = 95x
Now SP2 = 95x + 20% of 95x = 95x + 17x =114x
SP2 - SP1 = 80
⇒ 114x - 110x = 80
⇒ 4x = 80
⇒ x = 20
Initial Cost of table = 100 × 20 = Rs. 2000
68. A radio is sold for Rs. 990 at a profit of 10% . What would have been the actual profit or loss on it had it been sold for Rs. 890 ?
a) Rs. 10 loss
b) Rs. 10 profit
c) Rs. 90 loss
d) Rs. 90 profit
Discussion
Explanation: Selling price of a radio (SP) = Rs 990
profit (g) = 10%
Let the cost price = CP
$$\eqalign{ & {\text{CP}} = \frac{{{\text{SP}} \times 100}}{{100 + {\text{g}}}} \cr & \Rightarrow CP = \frac{{990 \times 100}}{{100 + 10}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{990 \times 100}}{{110}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,900 \cr & {\text{CP}} = Rs.\,900 \cr & {\text{SP}} = Rs.\,890 \cr & {\text{CP}} > {\text{SP}} \cr & {\text{He}}\,{\text{gets}}\,{\text{loss}} \cr & = {\text{Rs}}{\text{.}}\,900 - {\text{Rs}}{\text{.}}\,890 \cr & = {\text{Rs}}{\text{.}}\,10 \cr} $$
69. A man sells an article at 10% loss. If he had sold it at Rs. 10 more, he would have gained 10% . The cost price of the article is = ?
a) Rs. 50
b) Rs. 55
c) Rs. 100
d) Rs. 110
Discussion
Explanation: Let the CP1 of Article= 100x
Initial SP1 = 100x - 10% of 100x = 100x - 10x = 90x
If He sold the Article 10% profit
Now SP2 = 100x + 10% of 100x = 100x + 10x =110x
SP2 - SP1 = 10
⇒ 110x - 90x = 10
⇒ 20x = 10
⇒ x = $$\frac{1}{2}$$
Initial Cost of Article = 100 × $$\frac{1}{2}$$ = Rs. 50
70. By selling a bicycle for Rs. 2850, a shopkeeper gains 14% . If the profit is reduced to 8% then the selling price will be -
a) Rs. 2600
b) Rs. 2700
c) Rs. 2800
d) Rs. 3000
Discussion
Explanation: Let the new S.P. be Rs. x
then, 114 : 2850 = 108 : x
$$\eqalign{ & \Rightarrow x = \left( {\frac{{2850 \times 108}}{{114}}} \right) \cr & \Rightarrow x = 2700 \cr} $$
71. A trader sells an article and loses $$12\frac{1}{2}$$%. The ratio of cost price to the selling price is -
a) 7 : 8
b) 9 : 8
c) 8 : 7
d) 8 : 9
Discussion
Explanation:
$$\eqalign{ & {\text{Let C}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. }}x \cr & {\text{Loss}} = 12\frac{1}{2}\% \cr & {\text{S}}{\text{.P}}{\text{.}} = 87\frac{1}{2}\% {\text{ of Rs}}{\text{. }}x \cr & \,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\left( {\frac{{175}}{2} \times \frac{1}{{100}} \times x} \right) \cr & \,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\frac{{7x}}{8} \cr & {\text{Required ratio}} \cr & = x:\frac{{7x}}{8} = 8:7 \cr} $$
72. If the cost price of 18 articles is equal to the selling price of 16 articles, the gain or loss is = ?
a) 25% gain
b) 25% loss
c) $$12\frac{1}{2}$$% loss
d) $$12\frac{1}{2}$$% gain
Discussion
Explanation: 18 Cost Price = 16 Selling Price
$$\eqalign{ & \frac{{{\text{CP}}}}{{{\text{SP}}}} = \left. {\frac{{16}}{{18}} = \frac{8}{9}} \right\}{\text{1 unit profit}} \cr & {\text{Profit}}\% = \frac{1}{8} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 12\frac{1}{2}\% {\text{ gain}} \cr} $$
73. The price of a refrigerator and a television set are in the ratio 5 : 3. If the refrigerator costs Rs. 5500 more than the television set, then the price of the refrigerator is = ?
a) Rs. 27500
b) Rs. 8250
c) Rs. 13750
d) Rs. 16500
Discussion
Explanation:
$$\eqalign{ & \frac{{{\text{CP of Refrigerator}}}}{{{\text{CP of Television }}}}\left. { = \frac{5}{3}} \right\}{\text{2 unit }} \cr & {\text{2 unit}} = 5500 \cr & {\text{1 unit}} = \frac{{5500}}{2} = 2750 \cr & 5{\text{ units}} = 2750 \times 5 = 13750 \cr & {\text{Cost price of Refrigerator}} \cr & = {\text{Rs}}{\text{.13750}} \cr} $$
74. If books bought at prices from Rs. 150 to Rs. 300 are sold at prices ranging from Rs. 250 to Rs. 350. What is the greatest possible profit that might be made in selling 15 books ?
a) Cannot be determind
b) Rs. 750
c) Rs. 4250
d) Rs. 3000
Discussion
Explanation: Cost price of a book ranges between
= Rs. 150 to 300
Selling price of a book ranges between
= Rs. 250 to 350
For maximum profit cost price should minimum and Selling price should be maximum
Cost price = 150
Selling price = 350
Profit = Selling price - Cost price
= 350 - 150
= Rs. 200/book
Total profit on 15 books
= 200 × 15
= Rs. 3000
75. A person buys an article for Rs. p and sells it for Rs. q thereby gaining r% . The selling price in terms of cost price may be written as -
a) $$\frac{{{\text{pr}}}}{{100}}$$
b) $$\frac{{{\text{r}}\left( {100 + {\text{p}}} \right)}}{{100}}$$
c) $$\frac{{{\text{p}}\left( {100 + {\text{r}}} \right)}}{{100}}$$
d) $$\frac{{{\text{p}}\left( {100 - {\text{r}}} \right)}}{{100}}$$
Discussion
Explanation:
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. p}} \cr & {\text{Gain}} = {\text{r}}\% \cr & {\text{S}}{\text{.P}}{\text{.}} = {\text{q}} \cr & = \left( {100 + {\text{r}}} \right)\% {\text{ of Rs}}{\text{. p}} \cr & = \frac{{{\text{p}}\left( {100 + {\text{r}}} \right)}}{{100}} \cr} $$
76. The owner of a furniture shop charges his customer 28% more than the cost price. If a customer paid Rs. 23680 for a dining table set, then what was the original price of the dining set ?
a) Rs. 15700
b) Rs. 16250
c) Rs. 17500
d) Rs. 18500
Discussion
Explanation:
$$\eqalign{ & {\text{S}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. }}23680 \cr & {\text{Profit}} = 28\% \cr & {\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {\frac{{100}}{{128}} \times 23680} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}18500 \cr} $$
77. An article marked at Rs. 540 is sold at Rs. 496.80 in an off - season offer. Then the rate of discount offered (in percent) is = ?
a) 7%
b) 7.5%
c) 8%
d) 10%
Discussion
Explanation:
$$\eqalign{ & {\text{Discount}} \cr & = 540 - 496.80 \cr & = 43.2 \cr & {\text{Discount }}\% \cr & = \frac{{43.2}}{{540}} \times 100 \cr & = 8\% \cr} $$
78. Bhuvnesh sell two tape recorders at the same price. On one, he gains 10% and on the other he loses 10%. The total gain or loss in the transaction is=?
a) 1% gain
b) 1% loss
c) No loss or gain
d) 2% loss
Discussion
Explanation: In this type of question always loss
$$\frac{{P\% \times L\% }}{{100}} = \frac{{10 \times 10}}{{100}} = 1\% \,{\text{loss}}$$
79. A cloth merchant has announced 25% rebate in prices. If one needs to have a rebate of Rs. 40 then how many metres of cloth costing Rs. 32 per metre he should purchase =
a) 6m
b) 5m
c) 10m
d) 7m
Discussion
Explanation: Let x metre of cloth will be purchased.
$$\eqalign{ & x \times 32 \times \frac{{25}}{{100}} = 40 \cr & x \times 8 = 40 \cr & x = 5\,m \cr} $$
80. A shopkeeper expects a gain of $$22\frac{1}{2}$$% on his cost price. If in a week, his sale was of Rs. 392, what was his profit ?
a) Rs. 18.20
b) Rs. 70
c) Rs. 72
d) Rs. 88.25
Discussion
Explanation:
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{. = Rs}}.\left( {\frac{{100}}{{122.50}} \times 392} \right) \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\left( {\frac{{1000}}{{1225}} \times 392} \right) \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}320. \cr & {\text{Profit}} = {\text{Rs}}.\left( {392 - 320} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}72 \cr} $$
81. Cost price of 12 oranges is equal to the selling price of 9 oranges and the discount on 10 oranges is equal to the profit on 5 oranges. What is the percentage point difference between the profit percentage and discount percentage?
a) 20
b) 22.22
c) 16.66
d) 15
Discussion
Explanation: Ratio of selling price and Cost Price,
SP : CP = 12 : 9 =4 : 3
Profit of 3 oranges = Rs. 1 (Let CP = Rs. 1)
Profit = $$\frac{1}{3}$$ = 33.33%
Discount = 11.11%
CP : SP : MP = 3 : 4 : 4.5
Profit doubles that of discount.
So, % point discount = 33.33% - 11.11% = 22.22% point.
82. Profit on selling 10 candles equals selling price of 3 bulbs. While loss on selling 10 bulbs equal selling price of 4 candles. Also profit percentage equals to the loss percentage and cost of a candle is half of the cost of a bulb. What is the ratio of selling price of candles to the selling price of a bulb?
a) 5 : 4
b) 3 : 2
c) 4 : 5
d) 3 : 4
Discussion
Explanation: Candle - - - - - - - - Bulb
CP . . . . A - - - - - - - - B
SP . . . . C - - - - - - - - D
$$\eqalign{ & C = 2A \cr & {\text{Profit}} = 10\left( {B - A} \right) = 3D \cr & {\text{Loss}} = 10\left( {C - D} \right) = 4B \cr & {\text{Profit}}\% = \frac{{ {3D \times 100} }}{{10A}} \cr & {\text{Loss}}\% = \frac{{ {4B \times 100} }}{{10C}} \cr & {\text{Now,}} \cr & \frac{{ {3D \times 100} }}{{10A}} = \frac{{ {4B \times 100} }}{{10C}} \cr & \frac{B}{D} = \frac{3}{2} = 3:2 \cr} $$
83. An egg seller sells his eggs only in the packs of 3 eggs, 6 eggs, 9 eggs, 12 eggs etc., but the rate is not necessarily uniform. One day Raju (which is not the same egg seller) purchased at the rate of 3 eggs for a rupee and the next hour he purchased equal number of eggs at the rate of 6 eggs for a rupee. Next day he sold all the eggs at the rate of 9 eggs for Rs. 2. What is his percentage profit or loss?
a) 10% loss
b) 11.11% loss
c) 3% loss
d) 2.5% profit
Discussion
Explanation:
$$\eqalign{ & {\text{CP of one egg in }}{{\text{1}}^{st}}{\text{ case}} \cr & = \frac{1}{3} = 33.33\,{\text{paise}} \cr & {\text{CP of one egg in}}\,{2^{nd}}{\text{ case}} \cr & = \frac{1}{6} = 16.66\,{\text{paise}} \cr & {\text{Average}}\,{\text{CP}} \cr & = \frac{{ {33.33 + 16.66} }}{2} \cr & = 25\,{\text{paise}} \cr & {\text{Selling}}\,{\text{price}}\,{\text{of}}\,{\text{9}}\,{\text{eggs}} \cr & = Rs.\,2 \cr & {\text{SP}}\,{\text{of}}\,{\text{one}}\,{\text{egg}} \cr & = \frac{{200}}{9} \cr & {\text{Profit}}\,{\text{or}}\,{\text{loss}} \cr & = \frac{{ {\left( {25 - {\frac{{200}}{9}} } \right) \times 100} }}{{25}} \cr & {\text{Profit}}\,{\text{or}}\,{\text{loss}} \cr & = 11.11\,{\text{loss}} \cr} $$
84. Find the selling price of goods if two salesmen claim to make 25% profit each, one calculating it on cost price while another on the selling price, the difference in the profits earned being Rs. 100 and selling price being the same in both the cases?
a) Rs. 1200
b) Rs. 1600
c) Rs. 2400
d) Rs. 2500
Discussion
Explanation: Let CP's be Rs. 1000 each, their respective SP will be,
1000 == 25%↑ ⇒ 1250 [person calculating profit on the CP]
1000 == 33.33%↑ ⇒ 1333.33 [The person calculating his profit on SP: 25% of SP = 33.33% of CP]
The difference turned out to be = 83.33. This has occured when we have assumed the CP as 1000. But, we are given difference of Rs. 100
On comparing,
83.33 = 1000
1 = $$\frac{{1000}}{{83.33}}$$
100 = $$\frac{{1000}}{{83.33}} \times 100$$ = Rs. 1200
85. A shopkeeper calculate percentage profit on the buying price and another on the selling price. What will be their difference in profits if both claim a profit of 20% on goods sold for Rs. 3000?
a) Rs. 200
b) Rs. 100
c) Rs. 150
d) Rs. 400
Discussion
Explanation: For 20% profit on selling price means $$\frac{1}{5}$$ of 3000 i.e. Rs. 600
let CP = Rs. 100,
SP with 20% profit = Rs. 120
For 20% profit on selling price means cost is 100 + profit is 20 = selling price is 120.
Means selling price is 120% of cost price.
Now selling price is 120% ie 3000 then find 100% amount which will be cost.
Cost = $$\frac{{3000}}{{120}}\% $$
= $$\frac{{3000}}{{\frac{6}{5}}}$$
Because, 120% = $$\frac{6}{5}$$
= 3000 x $$\frac{5}{6}$$
= 2500
Cost is 2500
Thus profit is 20% i.e. $$\frac{1}{5}$$ x 2500 = 500
Difference is 600 - 500 = Rs.100
86. A pharmaceutical company made 3000 strips of tablets at a cost of Rs. 4800. The company gave away 1000 strips of tablets to doctors as free samples. A discount of 25% was allowed on the printed price. Find the ratio profit if the price is raised from Rs. 3.25 to Rs. 4.25 per strip and if at the latter price, samples to doctors were done away with. (New profit / Old profit).
a) 55.5
b) 63.5
c) 75
d) 99.25
Discussion
Explanation: Total sales revenue (Old) = 2000 × 3.25 × 0.75 = 4875 [0.75 as 25% discount was allowed]
Profitold = Total sales revenue - 4800
= 4875 - 4800 = 75
Total sales revenue (New) = 3000 × 4.25 × 0.75 = 9562.5 [New price is calculated on doctors samples as well.]
Profitnew = 9562.5 - 4800 = 4762.5
Ratio,
$$\frac{{{\text{Profi}}{{\text{t}}_{{\text{new}}}}}}{{{\text{Profi}}{{\text{t}}_{{\text{old}}}}}} = \frac{{4762.5}}{{75}} = 63.5$$
87. An article costing Rs. 20 was marked 25% above the cost price. After two successive discounts of the same percentage, the customer now pays Rs. 20.25. What would be the percentage change in profit had the price been increased by the same percentage twice successively instead reducing it?
a) 3600%
b) 3200%
c) 2800%
d) 4000%
Discussion
Explanation: The successive discounts must have been of 10% each As
20 (CP) == 25%↑ ⇒ 25(MP) == 10↓ ⇒ 22.5 == 10%↓ ⇒ 20.25(SP)
Profit = 20.25 - 20 = 0.25
Increased percentage if price have been increased twice successively instead of reducing it,
20(MP) == 10%↑ ⇒ 27.5 == 10%↑ ⇒ 30.25
Profit = 30.25 - 20 = 10.25.
Profit Change = 10.25 - 0.25 = 10
Percentage Profit change,
= $$\frac{{10 \times 100}}{{0.25}}$$
= 4000%
88. A pen company produces very fine quality of writing pens. Company knows that on average 10% of the produced pens are always defective so are rejected before packing. Company promises to deliver 7200 pens to its wholesaler at Rs. 10 each. It estimates the overall profit on all the manufactured pens to be 25%. What is the manufactured cost of each pen?
a) Rs. 6
b) Rs. 7.2
c) Rs. 5.6
d) Rs. 8
Discussion
Explanation: The company is able to deliver 90% of the manufactured pens. Means to produce 7200 pens they must have to produce 8000 pens as 10% are defectives.
So, let K be the manufacturing price of each pen.
Total income (including 25% profit) = 8000 × K × 1.25
This same income is obtained by selling 90% manufactured pens at Rs. 10 which is equal to 7200 × 10
8000 × K × 1.25 = 7200 × 10
K = Rs. 7.2 [90% of 8000 = 7200]
89. A company charges a fixed rental of Rs. 350 per month. It allows 200 calls free per month. Each call is charge at Rs. 1.4 when the number of calls exceed 200 per month and it charges Rs. 1.6 when the number of calls exceeds 400 per month and so on. A customer made 150 calls in February and 250 calls in march. By how much percent each call is cheaper in March than each call in February.
a) 28%
b) 25%
c) 18.5%
d) 16%
Discussion
Explanation:
$$\eqalign{ & {\text{Charge per call in February}} \cr & = \frac{{350}}{{150}} = \frac{7}{3} = 2.33 \cr & {\text{Charge per call in March}} \cr & = \frac{{ {350 + \left( {50 \times 1.4} \right)} }}{{250}} \cr & = \frac{{420}}{{250}} = \frac{{42}}{{25}} = 1.68 \cr & \% {\text{ Cheaper call rate in March}}. \cr & = {\frac{{ {2.33 - 1.68} }}{{2.33}}} \times 100 \cr & = 28\% \cr} $$
90. In the Bargaining Bazar everyone purchase with a fair bargaining, so the traders markup the prices too much. A trader marked up an article at Rs. M expected huge profit if it is sold on marked price. But a customer purchased it at $$\frac{{\text{M}}}{2}$$ with his fine bargaining skills, so the expected profit of the trader diminished by 66.66%. What is the percentage discount fetched by the customer through bargaining?
a) 33.33%
b) 50%
c) 60%
d) 66.66%
Discussion
Explanation:
$$\eqalign{ & {\text{MP}} = M \cr & {\text{SP}} = \frac{M}{2} \cr & \% \,{\text{Discount}} \cr & = {\frac{{ {\frac{M}{2}} }}{M}} \times 100 \cr & = 50\% \cr} $$
91. The price of an article reduces to 576 after two successive discounts. The markup is 80% above the cost price of Rs. 500. What is the new profit percentage if instead of two successive discounts the markup price was further increased successively two times by the same percentage?
a) 259.2%
b) 157%
c) 159.2%
d) 300%
Discussion
Explanation
$$\eqalign{ & {\text{CP}} = 500 \cr & {\text{SP}} = 576 \cr & {\text{MP}} = 900\left[ {80\% \,{\text{above}}\,{\text{the}}\,{\text{CP}}} \right] \cr & {\text{SP}} = {\text{MP}} \times {\left[ {1 - {\frac{R}{{100}}} } \right]^2} \cr & \left[ {{\text{R = Rate}}\,{\text{of}}\,{\text{Discount}}} \right] \cr & 576 = 900 \times {\left[ {1 - {\frac{R}{{100}}} } \right]^2} \cr & R = 20\% \cr & {\text{SP}} = {\text{MP}} \times {\left[ {1 + {\frac{R}{{100}}} } \right]^2} \cr & {\text{SP}} = 900 \times {\left[ {1 + {\frac{{20}}{{100}}} } \right]^2} \cr & {\text{SP}} = 1296 \cr & {\text{New}}\,{\text{Profit}}\,{\text{Percentage}}, \cr & = {\frac{{ {SP - CP} }}{{CP}}} \times 100 \cr & = {\frac{{ {1296 - 500} }}{{500}}} \times 100 \cr & = 159.2\% \cr} $$
92. A dishonest trader marks up his goods by 80% and gives discount of 25%. Besides he gets 20% more amount per kg from wholesaler and sells 10% less per kg to customer. What is the overall profit percentage?
a) 50%
b) 60%
c) 70%
d) 80%
Discussion
Explanation: CP = $$\frac{{100}}{{120}} = \frac{{10}}{{12}}$$ [He purchases 120 g and pays Rs. 100, by assumption actual CP of 1 g = Re. 1]
SP = $$\frac{{135}}{{90}} = \frac{3}{2} = \frac{{18}}{{15}}$$ [Actual MP = 180 as he mark up 80% above, SP = 135, with 25% discount and he sells 90 g instead of 100g]
Percentage Profit = $$ {\frac{{\frac{{18}}{{12}} - \frac{{10}}{{12}}}}{{\frac{{10}}{{12}}}}} \times 100 = 80\% $$
93. The profit percentage on three articles A, B and C is 10%, 20%, and 25% and the ratio of the cost price is 1 : 2 : 4. Also the ratio of number of articles sold of A, B and C is 2 : 5 : 2, then overall profit percentage is:The profit percentage on three articles A, B and C is 10%, 20%, and 25% and the ratio of the cost price is 1 : 2 : 4. Also the ratio of number of articles sold of A, B and C is 2 : 5 : 2, then overall profit percentage is:
a) 18.5%
b) 21%
c) 23%
d) 27%
Discussion
Explanation: Ratio of CP = 1 : 2 : 4
Let cost of,
A = x
B = 2x
C = 4x
Ratio of Number of sell = 2 : 5 : 2
Let number of items sold be,
A = 2y
B = 5y
C = 2y
Total cost (A + B + C),
= (2xy + 10xy + 8xy)
= 20xy
Profit of A = 0.2xy
Profit of B = 2xy
Profit of C = 2xy
Total profit = 4.2xy
% Profit = $$\frac{{4.2{\text{xy}} \times 100}}{{20{\text{xy}}}} = 21\% $$
94. The accountants of a company show sales of Rs. 12,600. The primary cost is 35% of sales and trading cost accounts for 25% of the gross profit. Gross profit is arrived at by excluding the primary cost plus the cost of advertising expenses of Rs. 1400, director's salary of Rs. 650 per annum plus 2% annual sales as miscellaneous costs. Find the percentage profit (approx) on a capital investment of Rs. 14,000?
a) 35%
b) 31%
c) 28%
d) 26%
Discussion
Explanation: Primary Cost:
35% of 12600 = 4410
Miscellaneous costs:
2% of 12600 = 252
Gross Profit = 12600 - 4410 - 1400 - 650 - 252 = 5888
Trading Cost = 0.25 × 5888 = 1472
Net Profit = 4416
% Profit =$$\frac{{4416}}{{14000}} \times100$$
= 31.54%
≈ 31%
95. A dishonest shopkeeper, at the time of selling and purchasing, weighs 10% less and 20% more per kilogram respectively. Find the percentage profit earned by treachery. (Assuming he sells at Cost Price)
a) 30%
b) 20%
c) 25%
d) 33.33%
Discussion
Explanation: While purchasing he would take 1200 grams for the price of 1000 grams. While selling he would sell 900 grams for the price of 1000 grams.
Since, CP = SP
Profit =
$$\frac{{{\text{Goods Left}}}}{{{\text{Goods Sold}}}} = \frac{{300 \times 100}}{{900}} = $$ $$33.33\% $$
96. David sells his Laptop to Goliath at a loss of 20% who subsequently sells it to Hercules at a Profit of 25%. Hercules, after finding some defect in the laptop, returns it to Goliath but could recover only Rs. 4.50 for every Rs. 5 he had paid. Find the amount at Hercules' loss if David had paid Rs. 1.75 lakh for the laptop.
a) 3500
b) 2500
c) 17500
d) 20000
Discussion
Explanation: David (100) == 20% ↓(loss) ⇒ Goliath (80) == 25% ↑(gain) ⇒ Hercules(100) == 10% ↓ (loss) ⇒ Goliath (90)
Hercules loss corresponds to 10 when David buys the laptop for Rs. 100.
Thus, Hercules loss would be Rs. 17,500 when David buys the laptop for 1,75,000.
97. The cost of servicing of a Maruti car at Maruti care Pvt. Ltd. is Rs. 400. Manager of service centre told me that for the second service within a year a customer can avail a 10% discount and further for third and fourth servicing he can avail 10% discount of the previous amount paid, within a year. Further if a customer gets more than 4 services within a year, he has to pay just 60% of the servicing charges on these services. A customer availed 5 services from the same servicing station, what is the total percentage discount fetched by the customer?
a) 19.42%
b) 18.5%
c) 17.6%
d) 26%
Discussion
Explanation: Amount paid in 1st service = 100 (Assume)
Amount paid in 2nd service = 90
Amount paid in 3rd service = 81
Amount paid in 4th service = 72.9
Amount paid in 5th service = 60
Total amount paid,
= (100 +90 +81 +72.9 +60) = 403.9
Total Discount = 500 - 403.9 = 96.1
% Discount = $$\frac{{96.1 \times 100}}{{500}}$$ = 19.42%
98. A vendor sells his articles at a certain profit percentage. If he sells his article at $$\frac{1}{3}$$ of his actual selling price, then he incurs a loss of 40%. What is his actual profit percentage?
a) 72%
b) 120%
c) 80%
d) 60%
Discussion
Explanation: 100 (CP) == 80%↑ ⇒ 180(SP)
$$\frac{1}{3}$$ of SP = $$\frac{180}{3}$$ = 60
Loss = 40% = 100 - 60 = 40
Hence, option (c) is correct as it gives 40% loss on CP on reducing the price to $$\frac{1}{3}$$ of CP.
99. Arun bought toffees at 6 for a rupee. How many for a rupee he should sell to gain 20%?
a) 2
b) 3
c) 4
d) 5
Discussion
Explanation: CP for one toffee = $$\frac{{100}}{6}$$
SP will be 20% above the CP.
SP for one toffee = $$\frac{{100}}{6} \times 1.2 = \frac{{100}}{5} = 20$$
Thus, He should sell 5 toffee for Rs. 1 (100 paise)
100. The cost price of 19 articles is same as the selling price of 29 articles. What is loss percentage?
a) 52.3%
b) 35%
c) 34.48%
d) 30%
Discussion
Explanation: Let CP of each article be Rs. 29 and SP of each article be Rs. 19
Loss Percentage
$$\eqalign{ & = \frac{{ {\left( {29x - 19x} \right) \times 100} }}{{29x}} \cr & = 34.48\% \cr} $$