Question 1

The profit earned after selling a pair of shoes for ₹ 2033 is the same as the loss incurred after selling the same pair of shoes for ₹ 1063. What is the cost price of the shoes?

Accepted Answer

Let the cost price of the shoes = ₹ x According to the question, 2033 - x = x - 1063 ⇒ 2x = 2033 + 1063 = 3096 ∴ x = 3096/2 = ₹ 1548

Question 2

A man sells an article at a profit of 40%. If he had bought it at 40% less and sold for ₹ 5 less, he would have gained 50% . Find the cost price of the article .

Accepted Answer

Let CP = ₹ 100, then SP = 140 New CP = ₹ 60 and new SP = (60 x 150)/100 ₹ 90 According to the question, ₹(140 - 90) = ₹ 50 is equivalent to ₹ 5. ∴ ₹ 100 is equivalent to ₹ 10. ∴ CP = ₹ 10

Question 3

A person sold his watch for ₹ 75 and got a percentage profit equal to the cost price. The cost price of the watch is.

Accepted Answer

Let CP of the watch be ₹ N. Then , According to the question, [(75 - N)/ N] x 100 = N ⇒ (75 - N) x 100 = N2 ⇒ N2 + 100N - 7500 = 0 ⇒ N2 + 150N - 50N - 7500 = 0 ⇒ N(N + 150) - 50 (N + 150) = 0 ⇒ (N + 150) (N - 50) = 0 ⇒ N = ₹ 50

Question 4

Two lots of onions with equal quantity, one costing ₹ 10 per kg and the other costing ₹ 15 per kg, are mixed together and whole lot is sold at ₹ 15 per kg. What is the profit or loss?

Accepted Answer

Let each lot of onion-contain N kg onion, Then total cost price of these two lots together = 10N + 15N = 25N Selling price of whole lot = 15 x (N + N) = 15 x 2N = 30N Profit percentage = [(30N - 25N)/25N] x 100 % = (5/25) x 100% = 20%

Question 5

A vender sells lemons at the rate of 5 for ₹ 14. gaining thereby 40%. For how much did he buy a dozen lemon?

Accepted Answer

SP of 1 lemon = ₹ 14/5 Let CP of 1 lemon = N According to the question, (N x 140)/100 = 14/5 ∴ N = ₹ 2 ∴ CP for 12 lemons = 12 x 2 = 24

Question 6

By selling 32 orange for ₹ 30 a man loses 25%. How many oranges should be sold for ₹ 24 so as to gain 20% in the transaction?

Accepted Answer

Let the cost price be ₹ N. SP of 1 orange = ₹ 30/32 = ₹ 15/16 According to the question, 75N/100 = 15/16 ∴ N = [(15 x 100)/75] x 16 = ₹ 5/4 SP of 1 orange with 20% profit = ₹ [(5/4) x 120]/100 = ₹ 3/2 ∴ In ₹ 3/2, the number of oranges sold = 1 ∴ in ₹ 24, the number of oranges sold = (2/3) x 24 = 16

Question 7

Kamlesh purchased 120 reams of paper at ₹ 100 per ream and the expenditure on transport was ₹ 480. He had to pay an octroi duty of 50 paise per ream and the coolie charges were ₹ 60. What should he charge per ream to gain 40%?

Accepted Answer

Total cost price = ₹ (120 x 100) = ₹ 12000 Total expenditure = 480 + (1/2) x 120 + 60 = ₹ 600 Total cost price = 12000 + 600 = ₹ 126000 Gain = 40% SP of 120 reams = 12600 x (140/100) = ₹ 17640 ∴ SP per ream = 17640/120 = ₹ 147

Question 8

A producer of a tea blends two varieties of tea from tea gardens one costing ₹ 18 per kg and another ₹ 20 kg in the ratio 5 : 3. If he sells the blended variety at ₹ 21 per kg, then his gain percentage is

Accepted Answer

Let quantities of two types of tea costing ₹ 18 per kg and ₹ 20 per kg be 5W kg and 3W kg. respectively. Then, CP of tea = (18 x 5W) + (20 x 3W) = 90W + 60W = 150W SP of tea = 21 x 8W = 168W Profit percent = [(168W - 150W) / 150W] x 100% = (18/150) x 100% = 12%

Question 9

Pens are bought at 5 for ₹ 4 and sold at 4 for ₹ 5. Find the gain per cent.

Accepted Answer

Let the number of pens bought = 5 x 4 = 20 Then, CP = (4/5) x 20 = ₹ 16 and SP = (5/4) x 20 = ₹ 25 ∴ Gain = 25 - 16 = ₹ 9 Gain % = (9/16) x 100% = 56.25%

Question 10

A person purchased 11 articles for ₹ 10 and sells at 10 articles for ₹ 11. Find the gain percentage.

Accepted Answer

Cost price of 11 Articles = 10 Cost price of 1 Article = 10/11 and SP of 10 Articles = 11 ∴ SP of 1 Article = 11/10 Now, gain = (11/10) - (10//11) = (121 - 100)/110 = 21/110 And gain% = [(21/110) / (10/11)] x 100 = (21 x 11)/11 = 21

Question 11

By selling 100 pens, a shopkeeper gains the selling price of 40 pens. Find his gain percent.

Accepted Answer

(SP of 100 pens) - (CP of 100 pens) = SP of 40 pens ⇒ SP of 60 pens = CP of 100 pens. Let CP of each pen = ₹ 1 Then, CP of 60 pens = ₹ 60 SP of 60 pens = ₹ 100 Gain = 100 - 60 = ₹ 40 ∴ Gain % = (40/60) x 100 % = 66.67%

Question 12

If the cost of price of 16 pens is equal to the selling price of 12 pens, then the gain or loss per cent is

Accepted Answer

Here, a = 16, b = 12 According to the formula, Required gain percent = [(a - b)/b] x 100 = [(16 - 12)/12] x 100 = (4/12) x 100 = 331/3% (gain)

Question 13

A dishonest dealer sells his goods at 10% loss on cost price but uses 20% less weight. What is his profit or loss per cent?

Accepted Answer

Here, a = 10% and b = 20% According to the formula, Required answer= [b ± a/(100 - b)] x 100 % = (20 - 10)/(100 - 20 ) x 100% = (10/80) x 100% = 12.5 % gain + ve sign show that profit is earned here.

Question 14

A trader sells wheat at 20% profit and uses weight 20% less than the actual measure. His gain per cent is?

Accepted Answer

Let the market weight = 1 kg = 1000 g Real weight = 80% of 1000 = 800 g Let the CP of 1 g = ₹ 1 ∴ CP of 800 g = ₹ 800, CP of 1000 g = ₹ 1000 SP = 120% of 1000 = (120/100) x 1000 = ₹ 1200 Gain = 1200 - 800 = ₹ 400 ∴ Gain % = (400/800) x 100% = 50%

Question 15

A dishonest dealer sells his goods at 10% loss on cost price and uses 30% less weight. What is his profit or loss per cent?

Accepted Answer

Given that, a = 10% and b = 30% According to the formula, Required per cent = [(b - a)/(100 - b)] x 100 = [(30 - 10)/(100 - 30)] x 100 = (20/70) x 100 = 200/7% = 284/7% profit

Question 16

A dishonest dealer professes to sell his goods at cost price but he uses a weight of 920 g for 1 kg weight. Find his gain per cent

Accepted Answer

According to the formula, Gain% = [Error / (True value - Error)] x 100% = [80/(100 - 80)] x 100% = (80/920) x 100% = 816/23 %

Question 17

A dealer sells goods at 4% loss on cost price but he uses 28 g instead of 32 g. What is his per cent profit or loss?

Accepted Answer

Given that, a = 4%, b = 28 g and c = 32 g Required profit = [(100 - a) x (c/b) -100] % =[(100 - 4) x (32/28) - 100] % = [96 x (32/28) - 100]% = [(96 x 8)/7 - 100]% = (768 - 700)/7 % = 68/7 % = 95/7 % gain + ve sign shows that profit is earned here.

Question 18

If the cost price of 20 articles is equal to the selling price of 15 articles, find the profit per cent.

Accepted Answer

Given that, a = 20 and b = 15 According to the formula, Profit %= [(a - b) / b] x 100 % = (5/15) x 100% = 100/3 % = 331/3%

Question 19

A furniture seller sells two tables ₹ 1500 each. He earned a profit of 20% on one table and suffered a loss of 20% on the another table. Net profit or loss in this deal is

Accepted Answer

Required loss = (a/10)2% = (20/10)2% = 4% Thus, seller gets 4% loss in the deal.

Question 20

If an article is sold at a gain of 6% instead of at loss of 6%, then the seller gets ₹ 6 more. The cost price of the article is

Accepted Answer

Let CP of the article be ₹ N, Then 106% of N - 94% of N = 6 ⇒ 12% of N = 6 ∴ N = (6 x 100)/12 = ₹ 50

Profit and Loss Questions