GMAT / GRE Mathematics Tutorial Series: Profit & Loss

Questions based on Profit and Loss are quite common in entrance exams (like GMAT, GRE and CAT) and this concept is an integral component of the MBA syllabus, including Accounting, Financial Statements, and more.

In this article, the basic concepts are first explained, followed by solved examples and practice questions.

Definitions and Formulas

  • Cost price (CP): The price at which a person buys a product.
  • Selling/Sales price (SP): The price at which a person sells a product.
  • Profit or Gain:  When a person sells a product at a price greater than its cost price, a profit is earned. That is, if SP > CP, then the difference between them is called profit.

Profit/Gain = SP (Selling Price) – CP (Cost Price)

  • Loss: When a person sells a product at a price lesser than its cost price, a loss is incurred. That is, if SP < CP, then the difference between them is called loss.

                                               Loss = Cost price (CP) – Selling Price (SP)

  • Profit or Loss Questions is always calculated on the cost price.
  • Marked price: Marked price, also known as the listed price is the price marked as the selling price of the product.
  • Discount or Rebate: The discount on the product is calculated on the marked price.

 These are a few of the basic formulas used in solving questions on profit and loss:

  • Gain % = (Gain / CP) * 100
  • Loss % = (Loss / CP) * 100
  • SP = [(100 + Gain%) / 100] * CP
  • SP = [(100 – Loss %) / 100]*CP

The above two formulas can also be written as,

  • If a product is sold at a gain of 10%, then SP = 110% of CP.
  • If a product is sold at a loss of 10%, then SP = 90% of CP.

CP = [100 / (100 + Gain%)] * SP

CP = [100 / (100 – Loss%)] * SP

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Solved Examples

Question 1: A chair is purchased for Rs. 450 and sold for Rs. 500. What is the gain percent?

Solution:

Gain = SP – CP = 500 – 450 = 50.

Gain% = (50/450)*100 = 100/9 %

Question 2: A man sold a table for Rs. 465. What is the cost price if a loss of 7% was incurred?

Solution:

CP = [100 / (100 – Loss %)] * SP

Therefore, the cost price of the table = (100/93)*465 = Rs. 500

Question 3: In a certain business deal, the profit percentage is set at 80% of the cost. If the cost further increases by 20% but the selling price remains the same, by how much does the profit percentage decrease?

Solution:

Let us assume CP = Rs. 100.

Then Profit = Rs. 80 and selling price = Rs. 180.

The cost increases by 20%, therefore,  New CP = Rs. 120, SP = Rs. 180.

Profit % = 60/120 * 100 = 50%.

Therefore, Profit decreases by 30%.

Question 4: A man bought a few pencils at the rate of 10 pencils for Rs. 40 and sold them at 8 pencils for Rs. 35. Find his gain or loss percent.

Solution:

Cost price of 10 pencils = Rs. 40 → CP of 1 pencil = Rs. 4.

Selling price of 8 pencils = Rs. 35 → SP of 1 pencil = Rs. 35/8

Therefore, Gain = 35/8 – 4 = 3/8.

Gain percent = (3/8)/4 * 100 = 9.375%

Question 5: The cost price of 10 candles is the same as the selling price of ‘n’ candles. If a loss of 40% is incurred, what is the approximate value of ‘n’?

Solution:

Let the price of each candle be Re. 1.

Then the cost price of n candles is Rs. n and

the selling price of n candles is Rs. 10.

Loss = n-10.

Loss of 40% → (loss/CP)*100 = 40

Therefore, [(n-10)/n]*100 = 40 → n = 17 (approx.)

Question 6: A dishonest vendor sells his groceries using weights that are 15% less than the actual weights and makes a profit of 20%. What is his total gain percentage?

Solution:

Let us consider a 1 kg bag of groceries. The actual weight of the grocery bag is 85% of 1000 gm = 850 gm.

Let the cost price of each gram be Rs. 1. Then the CP of each bag of grocery = Rs. 850.

SP of 1 kg of bag of grocery = 120% of the true CP

Therefore, SP = 120/100 * 1000 = Rs. 1200

Gain = 1200 – 850 = 350

Hence Gain % = 350/850 * 100 = 41.17%

Question 7: Ramesh bought two shirts for Rs. 2500 each. If he sells one at a profit of 5%, then for how much should he sell the other shirt to make a profit of 20% on the whole?

Solution:

Before we start, it’s important to note that it is not 15% to be added to 5%, to make it a total of 20%.

Let the other profit percent be x.

Therefore as per the following equation,

105/100 * 2500 + [(100+x)/100] * 2500 = 120/100 * 5000 → x= 35.

Hence, if he makes a profit of 35% on the second shirt, it comes to a total of 20% profit on the entire sale.

Question 8: A businessman gives a discount of 10% on the marked price and still gains 17% on the whole. At what percent above the cost price did he mark his products?

Solution:

Let the cost price be 100. Then SP = 117.

Let the marked price be x.

Therefore, 90% of x = 117 → x = 130.

Therefore, he marked his products at 30% above the cost price.

Question 9: A vendor marks a discount of 20% on the selling price of carpets. For a special sale day, he offers an additional discount of 25% after the first discount. If the carpet was sold for Rs. 3600, find

  • The marked price of the carpet and
  • The cost price if the vendor still makes a profit of 80% on the whole after all discounts is applied.

Solution:

Assume that the marked price of the article is x.

20% discount is given initially, followed by another discount of 25%.

So, 75% of 80% of x = 3600

75/100 * 80/100 * x = 3600 → x = 6000.

So the carpet was marked at Rs. 6000.

Cost price of the carpet = [100/ (100+80)]*3600 = Rs. 2000.

It is important to note that this DOES NOT equal to a 45% discount on the whole. When different discounts are applied successively, they CANNOT be added.

Also Check GMAT / GRE Tutorial Series Quadratic Equation

Practice Questions with solutions

 1) Calculate the loss percent when the loss incurred is 3/5th of the selling price?

  • A. 37
  • B. 37.5
  • C. 37.75
  • D. None

Answer: B

Explanation: Let the selling price be x. loss is 3x/5.

CP= SP+ loss = x + 3x/5 = 8x/5

Loss% = (3x/5) / (8x/5) * 100 = 37.5%

2) After applying successive discounts of 10% and 5% on a book, it was sold at Rs. 513. Find the marked price of the book.

  • A. Rs. 590
  • B. Rs. 600
  • C. Rs. 603.5
  • D. None

Answer: B

Explanation: 90/100 * 95/100 * x = 513 → x = 600

3) Arun sells a bag to Bala for Rs. 300 at a profit of 25%. Bala sells it to Kumar at a loss of 10%.

i) What was the original price paid by Arun?
ii) What was the price paid by Kumar to Bala?

  • A. 240, 260
  • B. 250, 270
  • C. 250, 260
  • D. 240, 270

Answer: D

Explanation: i) Price paid by Arun (cost price paid by Arun) = [100/(100+25)]*300 = Rs. 240.

  1. ii) Price paid by Kumar (Selling price by Bala to Kumar) = [(100-10)/100]*300 = Rs. 270.

 

4) A dealer sold two computers for Rs. 18,000 each. He gains 25% on one computer and loses 25 % on the other computer. What is his loss or gain percent?

  • A. 6.25 % gain
  • B. 6.25% loss
  • C. No profit no loss
  • D. 4% loss
  • E. 4% profit

 

Answer: B
Explanation: Profit and loss formula
Loss % = x2/100 = 625/100 = 6.25%

 

5) By selling his watch for Rs 600 more, Ajay could have made a profit of 5% on his sale instead of incurring a loss of 11%. What was his cost price?

  • A. Rs. 3750
  • B. Rs. 4000
  • C. Rs. 2250
  • D. Rs. 6,000
  • E. Rs. 4750

Answer: A
Explanation: CP = (Difference in SP) ÷ (% Difference in profit) = 600/(5-(-11)) × 100 = (600/16)×100 = Rs 3750

6) A salesman makes a profit of 20% by selling a suitcase. Find the profit percent if it were calculated on the selling price instead of the cost price?

  • A. 10 %
  • B. 20%
  • C. 30%
  • D. 16.67%
  • E. 12.5%

Answer: D
Explanation: If we assume CP = 100 then SP = 120. So the profit %, if calculated on SP will be
⇒ 20/120 × = 16.67%

7) An agent marks his goods at 25% above the cost price and allows his customers a 12 % reduction on their bills. What percent profit does he make?

  • A. 14 %
  • B. 10%
  • C. 18%
  • D. 12.5%
  • E. 12%

Answer: B
Explanation: Let CP= Rs. 100, therefore, MP= Rs. 125, Discount% = 12%
SP = 88% of MP = 88% of 125 = Rs. 110. Profit = 110 – 100 = Rs. 10
Profit = 10%.

8) In order to maintain the price line, a dealer offers a discount of 12 % on the marked price of cars in his showroom. However, he still manages to make a gross profit of 32 % on the cost price. Find the profit percent he would have made on the selling price had he sold his cars at the marked price.

  • A. 28.07 %
  • B. 50 %
  • C. 31.21 %
  • D. 23 %
  • E. 40%

Answer: B

Explanation: Let CP = 100. SP = 132. This price is with the discount of 12%, thus the marked price must be 132/0.88 = 150. Thus he is marking his cars at a price 50% above the cost price. Hence the profit will be 50%. 

9) A baker makes a profit of 10% by selling cakes at a certain price. If he charges Rs. 1.4 more per cake he would gain 30%. Find the original price of each cake.

  • A. Rs. 6
  • B. Rs. 5.80
  • C. Rs. 6.25
  • D. Rs. 6.70
  • E. Rs 7.70

Answer: E

Explanation: Rs. 1.4 is the increase in price and 20% is the increase in percentage. Thus those two can be equated. Hence it can be concluded that 1.4 is 20% of the price i.e. the CP of one cake is 1.4/0.20 = Rs. 7. The SP per cake in the first case is 7 × 1.1 = Rs. 7.70. Hence option is E. 

10) What profit percent is made by selling a clock at a particular price if by selling at four-fifth of that price there may be a loss of 12 %?

  • A. 10 %
  • B. 25 %
  • C. 42 %
  • D. 20 %
  • E. 35%

Answer: A

Explanation: Such question can be better answered by solving it in reverse order.

Assuming the CP = 100, a loss of 12% is incurred in the final case i.e. SP = 100 – 12 = Rs 88. Rs. 88 is four-fifth of the selling price according to the question.

The original selling price is, 88 × 5/4 = Rs. 110. CP =100. This means there is a profit of Rs. 10. This implies that the profit is 10% as we assumed the CP to be Rs 100.

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