Q: A man perchases certain number of toffees at 6 per rupee. and the same number of toffees at 7 per rupee. He mixed the toffs and sells them at 6 per rupee. What is his gain or loss percent?

CP of 1 toffee for 1st rate = 1/6 CP of 1 toffee for 2nd rate = 1/7 CP of 2 toffee after mixing = 1/6 + 1/7 = 13/42 CP of 1 toffee after mixing = 13/84 SP of 1 toffee after mixing = 1/6 Gain = 1/6 - 13/84 = 1/84 Gain% = [(1/84) / (13/84)] x 100% = 100/13% = 79/13%

Q: Raj sold an item for ₹ 6384 and incurred a loss of 30%. At what price should he have sold the item to have gained a profit of 30%

CP = 100/70 = x 6384 = ₹ 9120 To gain 30%, SP = 130% of 9120 SP = (130/100) x 9120 = ₹ 11856

Q: Niraj incurred a loss of 55% on selling an article for ₹ 9549. What was the cost price of the article?

Let cost price of article is CP. According to the formula, CP = [SP/(100 - Loss %)] x 100 CP = [(100 x 9549)/(100 - 55)] = ₹ 21220

Q: Find the percentage loss when the cost price and selling price of an article are in the ratio of 5 : 3.?

Let CP = 5N and SP = 3N Loss = (CP- SP) = (5N - 3N) = 2N Loss % = (2N / 5N) x 100 % = 40%

Q: A shopkeeper sells eggs at 20 for a rupee gaining 30%. How many eggs did he buy for a rupee?

SP of 20 eggs = ₹ 1 and gain = 30% CP of 20 eggs = (1 x 100)/130 = ₹ 10/13 Now, ₹ 10/13 yields 20 eggs. ∴ ₹ 1 will yield (20 x 13)/10 = 26 eggs Clearly, 26 eggs were bought for ₹ 1.

Question 1

A man sold an article for ₹ 322, gaining 1/6th of his outlay. Find the cost price of the article?

Accepted Answer

Let CP = N, then gain = N/6 According to the question, N + N/6 = 322 ⇒ 7N/6 = 322 ∴ N = 322 x 6/7 = ₹ 276

Question 2

The cost price of an item is two third of the selling price. What is the gain of loss per cent on that item?

Accepted Answer

let SP = N, then CP = 2N/3 Gain = (N - 2N/3) = N/3 &ther4; Gain % = [(N/3) / (2N/3)] x 100% = (N/3) x (3/2N) x 100% = 50%

Question 3

The difference between the CP and SP of the article is ₹ 240. If the profit is 20%, the selling price is?

Accepted Answer

Given, gain% = 20 Different between SP and CP = 240 Now, gain% = [(SP - CP)/ CP] x 100 ⇒ 20 = [240/CP] x 100 ⇒ CP = 240 x 5 ⇒ CP = 1200 ∴ SP = 1200 + 240 [∵ SP - CP = 240] = 1440

Question 4

Punkaj purchased an item for ₹ 7500 and sold it at the gain of 24%. Find the amount he purchased another item and sold it at the loss of 20%. What is his over all gain/ loss?

Accepted Answer

CP1 =₹ 7500 ∴ SP1 = (7500 x 124)/100 = ₹ 9300 = CP2 SP2 = (9300 x 80)/100= ₹ 7440 ⇒ CP1 > SP1 Hence, loss is incurred in this transaction ∴ Require loss = (CP1 - SP2) = 7500 - 7440 = ₹ 60

Question 5

Sumit purchased an item for ₹ 4000 and sold it at the gain% of 35%. From that amount, he purchased another item and sold it at the loss of 20%. What is his over all gain/loss?

Accepted Answer

CP1 = ₹ 4000 SP1 = 4000 x 135/100 = ₹ 5400 CP2 SP2 = 5400 x 80/100 = ₹ 4320 CP1 < SP2 Hence, profit earned here. ∴ Required gain = ( SP2 - CP1) = 4320 - 4000 = ₹ 320

Question 6

A man perchases certain number of toffees at 6 per rupee. and the same number of toffees at 7 per rupee. He mixed the toffs and sells them at 6 per rupee. What is his gain or loss percent?

Accepted Answer

CP of 1 toffee for 1st rate = 1/6 CP of 1 toffee for 2nd rate = 1/7 CP of 2 toffee after mixing = 1/6 + 1/7 = 13/42 CP of 1 toffee after mixing = 13/84 SP of 1 toffee after mixing = 1/6 Gain = 1/6 - 13/84 = 1/84 Gain% = [(1/84) / (13/84)] x 100% = 100/13% = 79/13%

Question 7

Raj sold an item for ₹ 6384 and incurred a loss of 30%. At what price should he have sold the item to have gained a profit of 30%

Accepted Answer

CP = 100/70 = x 6384 = ₹ 9120 To gain 30%, SP = 130% of 9120 SP = (130/100) x 9120 = ₹ 11856

Question 8

Niraj incurred a loss of 55% on selling an article for ₹ 9549. What was the cost price of the article?

Accepted Answer

Let cost price of article is CP. According to the formula, CP = [SP/(100 - Loss %)] x 100 CP = [(100 x 9549)/(100 - 55)] = ₹ 21220

Question 9

Find the percentage loss when the cost price and selling price of an article are in the ratio of 5 : 3.?

Accepted Answer

Let CP = 5N and SP = 3N Loss = (CP- SP) = (5N - 3N) = 2N Loss % = (2N / 5N) x 100 % = 40%

Question 10

A shopkeeper sells eggs at 20 for a rupee gaining 30%. How many eggs did he buy for a rupee?

Accepted Answer

SP of 20 eggs = ₹ 1 and gain = 30% CP of 20 eggs = (1 x 100)/130 = ₹ 10/13 Now, ₹ 10/13 yields 20 eggs. ∴ ₹ 1 will yield (20 x 13)/10 = 26 eggs Clearly, 26 eggs were bought for ₹ 1.

Question 11

A man brought toffees at 6 for a rupee. How many toffees for a rupee must he sell to gain in 50%.?

Accepted Answer

CP of 6 toffees = ₹ 1, SP of 6 toffees = 150% of 1 = 150/100 = 3/2 ∵ For ₹ 3/2, the number of toffees sold = 6 ∴ For ₹ 1, the number of toffees sold = 6 x (2/3) = 4

Question 12

A merchant fixed the selling price of his articles at ₹ 700 after adding 40% profit to the cost price. As the sale was very low at this price level, he decided to fix at the selling price at 10% profit. Find the new selling price

Accepted Answer

Let cost price = ₹ N According to the question, N x [(100 + 40)/100] = 700, ⇒ N = (700 x 100)/140 = 500 ∴ New selling price = 500 x (100 + 10)/100 = 5 x 110 = 550 = ₹ 550

Question 13

By selling a cellphone for ₹ 2400, a shopkeeper make a profit of 25%. Then, his profit percentage, if he had sold it for ₹ 2040, is

Accepted Answer

SP of cellphone = ₹ 2400 ∴ CP of cellphone = 2400 x [100/(100 + 25)] = ₹ 1920 ∴ Required percentage profit = [(2040 - 1920)/1920] x 100 = 6.25%

Question 14

Rajdeep loses 20% by selling a radio for ₹ 768. What percent will he gain by selling if for ₹ 1020?

Accepted Answer

SP = ₹ 768 and loss = 20% ∴ CP = (100/80) x 768 = (5/4) x 768 = ₹ 960 Now, CP = ₹ 960 and SP = ₹ 1020 Gain = 1020 - 960 = ₹ 60 ∴ Gain% = (60/960) x 100% = 6.25%

Question 15

A trader buys some goods for ₹ 150. If the overhead expenses be 12% of the cost price, at what price should it be sold to earn 10%?

Accepted Answer

Total CP = (CP + Overhead expenses) = 150 + 12% of 150 = 150 + (12/100) x 150 = ₹ 168 Given that, gain = 10% ∴ SP = (110/100) x 168 = ₹ 184.80

Question 16

If a watch is sold for ₹ 120, there is a loss of 15%. For a profit of 2%, the watch is to be sold for

Accepted Answer

SP = ₹ 120 and loss = 15% ∴ CP = (100/85) x 120 = 2400/17, Gain = 2% ∴ Required SP = (102/100) x (2400/17) = ₹ 144

Question 17

A person sold an article for ₹ 3600 and got a profit of 20%. Had he sold the article for ₹ 3150, how much profit would he have got?

Accepted Answer

Let the cost price of the article be ₹ N. Now, N + 20N/100 = 3600 ⇒ 120N/100 = 3600 ∴ N = 3000 Now, profit percentage when the article is sold for ₹ 3150 = [(3150 - 3000)/3000] x 100 = (150/3000) x 100 = 5%

Question 18

Meera purchased 23 bracelets at the rate of ₹ 160 per bracelet. At what rate per bracelet should she sell the bracelets so that profit earned is 15%?

Accepted Answer

Cost price of one bracelet = ₹ 160 Profit earned = 15% ∴ Selling price of one bracelet = Cost Price + Profit earned = 160 + (160 x 15)/100 = 160 + (16 x 15)/10 = 160 + 240/10 = 160 + 24 = 184 = ₹ 184 Hence, Meera should sale her bracelet ₹ 184 per piece.

Question 19

An article is sold for ₹ 300 at a profit of 20%. Had it been sold for ₹ 235, the loss percentage would have been?

Accepted Answer

Let the cost price of article = ₹ N Then, 120% of N = 300 ⇒ (120 x N)/100 = 300 ∴ N = (300 x 100)/120 = ₹ 250 Now, SP = ₹ 235 Then, loss percentage = [(250 - 235)/250 ] x 100 = 6%

Question 20

Neeta got profit of 10% on selling an article in ₹ 220. To get the profit of 30%, she should sell the article in how many rupees?

Accepted Answer

Let cost price of an article = (220 x 100)/110 = ₹ 200 For getting the profit of 30%, Selling price of an article = 130% of ₹ 200 = (130/100) x 200 = ₹ 260

Profit and Loss Questions