Profit and Loss Problems and Solutions | GMAT GRE Maths Tutorial

Before you delve into Profit and Loss concepts, take a few minutes to read this first and understand what every international student should know about building a good credit score.

Profit and Loss problems are directly relevant for not only entrance exams (like GMAT, GRE, CAT), but also for the MBA syllabus like Accounting, Financial Statements and more. In this article we cover the basic definitions, formulas, solved examples and wrap it up with some practice questions.

 

Profit and Loss | Definitions, Formulas, Solved Problems

 

Basic Definitions and Formulas

  • Cost price (C.P.): This is the price at which an article is purchased.
  • Selling price (S.P.): This is the price at which an article is sold.
  • Profit or Gain: If the selling price is more than the cost price, the difference between them is the profit incurred.

Formula: Profit or Gain = S.P. – C.P.

  • Loss: If the selling price is less than the cost price, the difference between them is the loss incurred.

Formula: Loss = Cost price (C.P.) – Selling Price (S.P.)

  • Profit or Loss is always calculated on the cost price.
  • Marked price: This is the price marked as the selling price on an article, also known as the listed price.
  • Discount or Rebate: This is the reduction in price offered on the marked or listed price.

Below is the list of some 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 be stated as,

If an article is sold at a gain of 10%, then SP = 110% of CP.

If an article is sold at a loss of 10%, then SP = 90% of CP.

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

 

Profit and Loss: Solved Examples

Question 1: An article is purchased for Rs. 450 and sold for Rs. 500. Find the gain percent.

Solution:

Gain = SP – CP = 500 – 450 = 50.

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

 

Question 2: A man sold a fan for Rs. 465. Find the cost price if he incurred a loss of 7%.

Solution:

CP = [100 / (100 – Loss %)] * SP

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

 

Question 3: In a transaction, the profit percentage is 80% of the cost. If the cost further increases by 20% but the selling price remains the same, how much is the decrease in profit percentage?

Solution:

Let us assume CP = Rs. 100.

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

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

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

Therefore, Profit decreases by 30%.

 

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

Solution:

Cost price of 10 toys = Rs. 40 → CP of 1 toy = Rs. 4.

Selling price of 8 toys = Rs. 35 → SP of 1 toy = 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 pens is the same as the selling price of n pens. If there is a loss of 40%, approximately what is the value of n?

Solution:

Let the price of each pen be Re. 1.

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

the selling price of n pens 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 merchant sells his grocery using weights 15% less than the true weights and makes a profit of 20%. Find his total gain percentage.

Solution:

Let us consider 1 kg of grocery bag. Its actual weight is 85% of 1000 gm = 850 gm.

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

SP of 1 kg of bag = 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: A man bought two bicycles for Rs. 2500 each. If he sells one at a profit of 5%, then how much should he sell the other so that he makes a profit of 20% on the whole?

Solution:

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

Let the other profit percent be x.

Then, our equation looks like this.

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

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

 

Question 8: A shopkeeper allows a discount of 10% on the marked price and still gains 17% on the whole. Find at what percent above the cost price did he mark his goods.

Solution:

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

Let the marked price be x.

So, 90% of x = 117 → x = 130.

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

 

Question 9: A shopkeeper offers a discount of 20% on the selling price. On a special sale day, he offers an extra 25% off coupon after the first discount. If the article was sold for Rs. 3600, find

  1. The marked price of the article and
  2. The cost price if the shopkeeper still makes a profit of 80% on the whole after all discounts are applied.

Solution:

Let the marked price of the article be x.

First a 20% discount was offered, on which another 25% discount was offered.

So, 75% of 80% of x = 3600

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

So the article was marked at Rs. 6000.

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

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

Profit and Loss Quiz: Practice Questions


Problem 1: Click here

Answer 1: Click here


Problem 2: Click here

Answer 2: Click here


Problem 3: Click here

Answer 3: Click here


 
Learn how to solve:
Simple and compound interest problems
Speed, distance and time problems
Probability problems
Ratio and proportion
List of Maths Formulas
 

Click here to watch this insightful video.

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5 thoughts on “Profit and Loss Problems and Solutions | GMAT GRE Maths Tutorial”

  1. one person sold his radio at 10% loss. if he had sold for rs 45 more he would have made 5% profit. for how much did he sell the radio?

    ans with explanation plz.

    Reply
    • Let Cost price of A and B are a , b respectively.
      Now for A ,
      2400-a/2400 = 25/100
      After calculating a = 1800

      Again for B,
      2400-b/b = 25/100
      after calculation b = 1920

      So profit of A = 600(2400 – 1800)
      and Profit of B = 480(2400-1920)

      Hence difference between their profit = 120

      Hope this will help

      Reply
    • Given: Workings:

      Rs. % Rs. %
      SP x 90 (x+45) 105 (x+45)-x=(105-90)%
      -CP 100 100 45=15%
      ————————————————- 1%=3
      Profit -10 +5 Therefore 90%=3*90=270
      Therefore 105%=3*105=315, so he sell the radio at Rs.315/-

      Reply
    • Ans is- let just take the cp 100. So now we need to find the 10%of 100 and then we will subtract it from 100. So that’s the sp. Now as per the info given we need to sell the radio at such a price to gain 5%. So we will now use an equation to find the new sp. let the sp be x
      5% of x =45. 5x÷100=45.5x=4500. So x is 900.

      Reply
  2. A Man Purchased a cycle worth rupees 4000 and sold it on the profit of 12.5% to another man.If the new man who purchased the cycle sells it after using it for a year at the loss of 33.33%
    how much loss him

    Reply

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