## Profit and Loss Questions and Answers Part-1

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

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

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%

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%

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

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) $$33\frac{1}{3}$$%

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%

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

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%

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

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