1. 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
Explanation:
$$\eqalign{ & {\text{Gain}}\% \cr & = {\frac{{ {{\text{True}}\,{\text{Weight}} - {\text{False}}\,{\text{Weight}}} }}{{{\text{False}}\,{\text{Weight}}}}} \times 100 \cr & \frac{{100}}{9} = {\frac{{ {1 - x} }}{x}} \times 100 \cr & \frac{{ {1 - x} }}{x} = \frac{1}{9} \cr & 10x = 9 \cr & x = 0.9\,kg = 900\,gms \cr} $$
2. 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
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
3. 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%
Explanation: Let original CP = Rs. 100
Then, the Marked Price = 40% of 100 + 100 = 140
SP = 140 - 25% of 140 = 105
%Profit = $$\frac{{5 \times 100}}{{100}} = 5\% $$
4. 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
Explanation:
$$\eqalign{ & {\text{Let Initial Price of sugar was }}X. \cr & {\text{After Discount of }}5\% , \cr & {\text{the price of the sugar become}}, \cr & = X - 5\% \,of\,X \cr & = X - {\frac{{5X}}{{100}}} \cr & = \frac{{ {100X - 5X} }}{{100}} \cr & = \frac{{95X}}{{100}} \cr & {\text{Amount of sugar now,}} \cr & {\text{Buyer gets in }}Rs.608, \cr & = \frac{{608}}{{ {\frac{{95X}}{{100}}} }} \cr & = \frac{{ {608 \times 100} }}{{95}} \cr & {\text{Amount of sugar he gets - }} \cr & {\text{before the discount,}} \cr & = \frac{{608}}{X} \cr & \frac{{608}}{{ {\frac{{95X}}{{100}}} }} - \frac{{608}}{x} = 2 \cr & {\text{On}}\,{\text{Solving}} \cr & X = Rs.\,16 \cr & {\text{After discount price become}} \cr & = 16 - 5\% \,of\,16 \cr & = Rs.\,15.20 \cr} $$
5. 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
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%
6. 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
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%
$$\eqalign{ & {\text{Actual price}} \cr & = {\text{Rs}}.\left( {\frac{{100}}{{110}} \times 5500} \right) \cr & = {\text{Rs}}{\text{. }}5000. \cr & {\text{Expenditure on repairs}} \cr & = {\text{Rs}}.\left( {5500 - 5000} \right) \cr & = {\text{Rs}}{\text{. }}500 \cr} $$
7. 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
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
8. 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
Explanation: Selling price of a radio (SP) = Rs 990
profit (g) = 10%
Let the cost price = CP
$$\eqalign{ & {\text{CP}} = \frac{{{\text{SP}} \times 100}}{{100 + {\text{g}}}} \cr & \Rightarrow CP = \frac{{990 \times 100}}{{100 + 10}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{990 \times 100}}{{110}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,900 \cr & {\text{CP}} = Rs.\,900 \cr & {\text{SP}} = Rs.\,890 \cr & {\text{CP}} > {\text{SP}} \cr & {\text{He}}\,{\text{gets}}\,{\text{loss}} \cr & = {\text{Rs}}{\text{.}}\,900 - {\text{Rs}}{\text{.}}\,890 \cr & = {\text{Rs}}{\text{.}}\,10 \cr} $$
9. 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
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
10. 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
Explanation: Let the new S.P. be Rs. x
then, 114 : 2850 = 108 : x
$$\eqalign{ & \Rightarrow x = \left( {\frac{{2850 \times 108}}{{114}}} \right) \cr & \Rightarrow x = 2700 \cr} $$