Question 1

A person bought two articles for ₹ 1500 and ₹ 1000 respectively one he sold at a gain of 20%. At what price should he sell the other to get a profit of 16% on the whole transaction?

Accepted Answer

CP of first article is ₹ 1500, Gain=20% SP of first article = (120/100) x 1500 = ₹ 1800 Total CP = 1500 + 1000 = ₹ 2500 Total gain = 16% Total SP = (116/100) x 2500 = ₹ 2900 SP of second article = (2900 - 1800) = ₹ 1100 Thus, he should sell the second article at ₹ 1100.

Question 2

A manufacturer of a certain item can sell all he can produce at the selling price of ₹ 60 each. It costs him ₹ 40 in materials and labour to produce each item and he has overhead expanses of ₹ 3000 per week in order to operate that plant. The number…

Accepted Answer

Suppose the manufacturer should product produce x items. ∴ 60x - (40x + 3000) = 1000 ⇒ 20x = 4000 ⇒ x = 200

Question 3

A sold an article to B at a profit of 10% and B sells it to C at a loss of 10% of C paid 2079. How much money was paid by A?

Accepted Answer

Amount paid by B = ₹110 Amount paid by C = 110 x 90/100 = ₹ 99 Then, If C paid ₹ 99 then, A paid ₹ 100. If C paid ₹ 2079, then A paid = 2079 x (100/99) = ₹ 2100

Question 4

A showroom owner sells a leather jacket for ₹ P and claims to make a profit of 10%. He plans to have stall in the trade fair and marks the same jacket at ₹ 2P, at the stall, he allows a discount of 20%. What will be the percentage profit that he wil…

Accepted Answer

SP at the stall at the trade fair = 2P - 20% of 2P = 8P/5 CP of the jacket = (P x 100)/(100 + 10) = 10P/11 ∴ profit = 8P/5 - 10/11 = 38P/55 ∴ Profit per cent made at the trade fair = [(38P/55) / (10P/11)]x 100 = (38/5) x (1/10) x 100 = 76%

Question 5

Mr X bought a music system with 20% discount on the labelled price. Had he bought it with 25% discount, he would have saved ₹ 500. At what price did he buy the music system?

Accepted Answer

Let the actual price of music system = ₹ P The cost of music system to Mr. P after 20% discount= (80/100) x P = 4P/5 Cost of music system to Mr P after 25% discount = (75/100) x P = 3P/4 Then according to the question, 4P/5 - 3P/4 = 500 ⇒ (16P - 15P)/20 = 500 ∴ P = 20 x 500 = 10000 ∴ Cost of music system at 20% discount = (80 x 10000)/100 = ₹8000

Question 6

A shopkeeper sold an article for ₹ 6750 after giving a discount of 10% on the labelled price. He would have earned a profit of 50%, had there been no discount. What was the actual percentage of profit earned?

Accepted Answer

Market price = ₹ P and SP = P -10% of P = 9P/10 ∴ 9P/10 = 6750 ⇒ P = 7500 If SP = ₹ Rs.7500, then the CP would have been Rs.5000 due to 50% profit earned by the Shopkeeper. ∴ Actual percentage of profit by selling the article for ₹ 6750 = [(SP - CP)/CP] x 100 = [(6750 - 5000)/5000] x 100 = (1750/5000) x 100 = 35%

Question 7

A trader fixed the price of an article in such a way that by giving a rebate of 10% on the price fixed, he made a profit of 15% . If the cost of the article is ₹ 72. The fixed price on it, is?

Accepted Answer

Let the fixed price of article = ₹P Then, Selling price = 90% of P = (90 x P)/100 = ₹ 9P/10 Also, the selling price = 115% of 72 = ₹(115 x 72)/100 ⇒ (115 x 72)/100 = 9P/10 ∴ P = ₹ 92

Question 8

A shopkeeper marks his goods at such a price that he can deduct 20% for cash and yet make 20% profit. The marked price of an item which cost him ₹ 180 is?

Accepted Answer

CP = ₹ 180, gain = 20% ∴ SP = (120/100) x 180 = ₹ 216 Let the MP be ₹ P. Then, 80% of P = 216 ∴ (80/100) x P = 216 ⇒ P = (216 x 100)/80 = 270 Thus, MP is ₹ 270.

Question 9

A trader allows a discount of 10% on the marked price of an article. How much percentage above the cost price the article be marked to make a profit of 17%?

Accepted Answer

Let the CP be ₹ 100 and let MP be ₹ x above ₹ 100. Then, MP = ₹ (100 + x) and discount =10% ∴ SP = [(90/100) x (100 + x)] = ₹ 177 ⇒ x = 30 So, cost should be labelled at 30% above CP.

Question 10

Ravi purchased a scooter at 11/13th of its marked price and sold it at 10% more than its marked price. His gain per cent is?

Accepted Answer

Let the MP of a scooter = ₹ P ∴ CP of a scooter= ₹ 11P/13, Gain = 10% SP = (110/100) x P= ₹ 11P/10 Gain = SP - CP = (11P/10 - 11P/13) = (143P - 110P)/130 = ₹ 33P/130 Gain percentage = (33P/130) x (13/11P) x 100 % = 30%

Question 11

A dealer buys an article marked at ₹ 40000 with 20% and 10% off. He spends ₹ 1200 on its repairs and sells it for ₹ 30000. What is his gain or loss per cent?

Accepted Answer

CP. = (80% of 90% of ₹40000) + ₹(1200) = [(80/100) x (90/100) x 40000] + 1200 = (28800 + 1200) = ₹30000 ∴ CP = ₹30000 So, no gain no loss in the transaction.

Question 12

A dishonest dealer professes to sell his goods at cost price. But he uses a false weight of 900 g per 1 kg weight. Find his gain percent?

Accepted Answer

Gain percentage = [Error/(True value - Error)] x 100 % = [(100/(1000 - 100)] x 100 % = (100/900) x 100 % = 111/9%

Question 13

A shopkeeper sells wheat at a profit of 10% and uses weight which are 20% less than the actual weight. The total gain earned by him will be?

Accepted Answer

Let the actual price of per kg of wheat = ₹ . 100 Then, selling price = 110% of 100 = ₹ 110 Now, shopkeeper sell 20% less than actual weight so cost price to shopkeeper will be = 80% of 100 = (80 x 100)/100 = ₹ 80 Hence, required profit gained by shopkeeper = [(110 - 80)/80] x 100 = (30/80) x 100 = 37.5%

Question 14

What is the percentage profit made by selling an umbrella at a certain price, if by selling at 2/3rd of that price, there would be a loss of 10%?

Accepted Answer

Let the selling price for the umbrella is P. Cost price for the umbrella is Q. Now from question Q - 2P/3 = 10% of Q. ⇒ P = (3/2)(Q - 10% of Q) ⇒ P = (3/2) x (90/100) x Q ∴ P = 1.35 x Q. So % profit = [(1.35 x Q - Q)/Q]x100 % = 35 % profit.

Question 15

Charu purchased a dinner set at 3/10th of its selling price and sold it at 10% more than its CP. Find the gain per cent.?

Accepted Answer

Let SP = ₹ 100 ∴ CP = (3/10) x 100 = ₹ 30 New SP = (30 x 110)/100 = ₹ 33 Gain = 33 - 30 = ₹ 3 Gain % = (3/30) x 100% = 300/30 % = 10%

Question 16

The owner of a furniture shop charges his customer 18% more than the CP. if a customer paid ₹ 10207 for a dining table, then find its original price.

Accepted Answer

Original CP = [100/(100 + Gain%)] x SP = (108/118) x 10207 = ₹ 8650

Question 17

Meena purchased two fans each at ₹ 1200. She sold one fan at the loss of 5% and other at the gain of 10%. Find total gain or loss per cent?

Accepted Answer

Total CP = 2 x 1200 = ₹ 2400 SP of 5% loss = (95/100) x 1200 = ₹ 1140 SP at 10% gain = (110/100) x 1200 = ₹ 1320 Total SP = 1140 +1320 = ₹ 2460 ∴ Gain = 2460 - 2400 = ₹ 60 Gain % = (60/2400) x 100% = 2.5%

Question 18

A woman bought eggs at ₹ 30 per dozen, The selling price per hundred so as to gain 12% will be (in ₹)

Accepted Answer

12 egg cost ₹ 30 Then cost price of 1 eggs = 35 x 12 = #8377; 2.5 Cost price of 100 eggs = 25 x 100 = ₹ 250 Now, let the SP of 100 eggs ₹ N. Then [(SP - CP) / CP] x 100= profit % [(N - 250)/250] x 100 = 12 ⇒ (N - 250)/(2/5) =12 ⇒ N- 250 = (12 x 5)/2= 30 N = 250 + 30 = ₹ 280

Question 19

A man purchases as certain number of oranges at 4 a rupee and the same number of orange at 5 a rupees. He mixes them together and sells them at 4 a rupee. What is the gain or loss percent?

Accepted Answer

CP of 1 orange for 1st rate = ₹ 1/4 CP of 1 orange for 2nd rate ₹ 1/5 CP of 2 orange after mixing = 1/4 + 1/5 = ₹ 9/20. CP of 1 orange after mixing ₹ 9/20 X 2 = ₹ 9/40 SP Of 1 orange after mixing = ₹ 1/4 ∴ Gain = 1/4 - 9/40 = ₹ 1/40 ∴ Gain = (1/40 x 40/9 x 100)% = 100/9% = 111/9%

Question 20

A man gained 10% by selling an article for a certain price. If the sells it at double the price, then the profit made is?

Accepted Answer

Let CP of the article be ₹ N Then, SP = 110% of x = 1.1N If SP be double i.e., 2.2N, then Profit per cent= [(2.2N - N)/ N] x 100% = 120%

Profit and Loss Questions