Profit and Loss - Aptitude Questions and Answers

Profit is the financial gain earned when total revenue exceeds total expenses, and loss is the financial deficit incurred when total expenses exceed total revenue.

Formula:

Profit = Selling Price – Cost Price

Loss = Cost Price – Selling Price

Profit and Loss questions and answers are provided below for you to learn and practice.

Question 1: A person buys a pen from a wholesaler at Rs. 10 for 20 pens. He sells those pens at Rs. 10 for 15 pens. Find his profit or loss percent. 

Solution: 

CP for each pen = 10 / 20 = Rs. 0.50
SP for each pen = 10 / 15 = Rs. 2 / 3
Profit = SP - CP = Rs. (2 / 3) - 0.50 = Rs. 1 / 6
Therefore, profit percent = [ (1/6) / (0.50) ] x 100 = 33.334% 

Question 2: A dealer incurs a loss of 5 % if he sells an article for Rs. 1805. What price must he sell the article so as to gain 5 % on that article? 

Solution: 

Let the cost price of the article be Rs. C => SP = CP - Loss
1805 = C - 0.05 C
0.95 C = 1805
C = 1900
Therefore, to gain 5 %, SP = 1900 + (0.05 x 1900) = 1900 + 95 = Rs. 1995 

Question 3: If the cost price of an article is 67 % of the selling price, what is the profit percent? 

Solution: 

Let the selling price of the article be Rs. S
Cost price of the article = 67 % of S = 0.67 S
Profit = SP - CP = 0.33 S
Therefore, profit percent = (0.33 S / 0.67 S) x 100 = 49.25 % 

Question 4: A shopkeeper purchased two varieties of rice, 80 KG at Rs. 13.50 per KG and 120 KG at Rs. 16 per KG. The shopkeeper being greedy, mixed the two varieties of rice and sold the mixture at a gain of 16 %. Find the per KG selling price of the mixture. 

Solution: 

We are given that the shopkeeper bought 80 Kg at Rs. 13.50 per KG and 120 KG at Rs. 16 per KG.
Total cost price = (80 x 13.50) + (120 x 16) = 1080 + 1920 = Rs. 3000
total rice = 80 + 120 = 200 KG
Now, total selling price = Total cost price + 16 % of total cost price
Total selling price = 3000 + (0.16 x 3000) = Rs. 3480
Thus, selling price per KG = 3480 / 200 = Rs. 17.40 

Another method:

We can do this question by allegation also.  

(m - 13.50) / (16 - m) = 120 / 80
m = 15,
where 'm' is the per KG cost price of the mixture
Therefore, per KG selling price of the mixture = Rs. 15 + 16% of 15 = Rs. 17.40 

Question 5: A seller claims to sell at cost price but gives 750 gm for each KG. Find his gain percent. 

Solution : 

Profit percent = [ (True Value - Given Value) / Given Value ] x 100 %
Here, True Value = 1 KG = 1000 gm Given Value = 750 gm
Therefore, profit percent = [ (1000 - 750) / 750 ] x 100 = (250 / 750) x 100 = 33.334 % 

Question 6: A man sold two watches at the same price, one at a 10 % profit and the other at a 10 % loss. Find his overall gain or loss percentage. 

Solution: 

We know that if two articles are sold at the same selling price, one at a gain of A% and one at the loss of A%, then the seller always incurs a loss of (A / 10)2.
Loss percent = (10 / 10)2 = 1 % 

Long Method: 

Let the selling price of each watch be Rs. 99 S
Total SP = Rs. 198 S CP of first watch = SP - Profit = Rs. 99 S- 10 % of CP = Rs. 90 S
CP of second watch = SP + Loss = Rs. 99 S + 10 % of CP = Rs. 110 S
Total CP = Rs. 90 S + 110 S = Rs. 200 S
Loss = Total CP - Total SP = 200 - 198 = Rs. 2 S
Therefore, loss percent = (Loss / CP) x 100 = (2 S / 200 S) x 100 % = 1 % 

Question 7: A shopkeeper gives two successive discounts of 20 % and 10 % on surplus stock. Further, he also gives a 5 % extra discount on cash payments. If a person buys a shirt from the surplus stock and pays in cash, what overall discount percent will he get on the shirt? 

Solution: 

Let the marked price of the shirt be Rs. 1000
Price after first discount = Rs. 1000 - 20 % of Rs. 1000 = Rs. 1000 - 200 = Rs. 800
Price after second discount = Rs. 800 - 10 % of Rs. 800 = Rs. 800 - 80 = Rs. 720
Price after cash discount = Rs. 720 - 5 % of Rs. 720 = Rs. 720 - 36 = Rs. 684
Therefore, total discount = Rs. 1000 - 684 = Rs. 316
Overall discount percent = (316 / 1000) x 100 = 31.60 % 

Question 8: A dealer wants to mark the price of an article such that by offering a 5 % discount, he is able to get 33 % profit. Find the percent of CP above which the article should be marked. 

Solution: 

Let the cost price of the article be Rs. 100
Selling price of the article = Rs. 100 + 33% of CP = Rs. 133
Let the marked price be Rs. M
Selling price = Marked Price - Discount
133 = M - 0.05 M
133 = 0.95 M
M = 140
M - CP = 140 - 100 = 40
Therefore, percent of CP above which the article should be marked = (40 / 100) x 100 = 40 %