Profit and Loss Problems and Solutions | GMAT Maths Tutorial

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

If the loss incurred in a transaction is 3/5th of the selling price, find the loss percent.

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

Answer 1

B.

Explanation

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

Cost price = Selling price + loss = x + 3x/5 = 8x/5

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

Problem 2

After applying successive discounts of 10% and 5% on an article, it was sold at Rs. 513. Find the marked price of the article.

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

Answer 2

B.

Explanation:

90/100 * 95/100 * x = 513 → x = 600

Problem 3

A sells a set of books to B for Rs. 300 at a profit of 25%. B sells it to C at a loss of 10%.

i) What was the original price paid by A?
ii) What was the price paid by C to B?

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

Answer 3

D.

Explanation:

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

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


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76 Comments

  1. Babban says:

    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.

    • rakesh kumar urwasha says:

      x/90 = (x+45)/105
      x= 270

      • U M SUDHAKAR BABU says:

        In this problem, always asked for to find CP.because there are to SPs in the problem
        Formula
        CP- (more gain/diff in %’s)*100

      • sujit halder says:

        let cp=100
        then sp=90
        therefore (90+45)-100=5%
        then 100%=700(cp)
        to gain 5% profit he would sell at 700+(700*5/100)=735

    • sidharth says:

      If profit% of A and B are same on selling the articles at 2400 each , but A calculate his profit on s.p. while B calculate it on c.p. This profit is equal to 25% each . what is the difference between their profit?

      Plssss rply fassst

      • Shriyanka says:

        i guess it shud be rs 120

        • saby says:

          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

      • Kanika says:

        A incurred loss of 600 while B earned a profit of 480. So over all difference is 1080. however difference in magnitude is 120

    • Musa Ezaz says:

      300 is answer (I think)

    • shikha soni says:

      there is an formula for the rs. more…
      (sell more/profit-(-loss) )*100
      45/15 *100
      rs.300

    • Profit % – loss % = 45/-
      5% -(-10 %) = 45/-

      15% is equivalent to 45/-

      So 100% is equivalent to 300/-

      So he sell the radio at 10% loss = 270/-

    • Gaurav Sapkota says:

      Soln, Here,
      In first Case,

      Let the Sp be Rs. x
      Loss percent(L%)= 10%

      C.P1= 100/100-L%*sp
      =100/100-10*x
      =10/9x

      In second case,

      Sp=Rs.(45+x)
      P%=5%

      Cp2=100/100+5*(45+x)
      =100/105*45+x)
      =4500+100x/105

      We know that, In both cases the cp is equal ,
      so, 10/9x=4500+100x/105

      or,1050x=40500+900x
      or,1050x-900x=40500
      or,150x=40500
      or,x=40500/150
      or,x=Rs.270

      Thus, The Selling price is Rs. 270.

  2. Mani says:

    Let C.P be X , S.P is 0.9 X . To have profit of 5% New S.P should be 1.05X. This should be equal to 0.9X+45=1.05X. Solving this the value of X=300.

    he sold his radio for = 0.9*300= Rs. 270

    • KHAN says:

      Q) 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.

      Answers:

      1) x/90 = (x+45)/105
      x= 270

      2) there is an formula for the rs. more…
      (sell more/profit-(-loss) )*100
      45/15 *100
      rs.300

      MY ANSWER IS 300 SAMAE AS THE SECOND SOLUTION. NOT SURE WHICH ONE IS CORRECT
      would some one help me with this please

  3. fenny says:

    A VCR is sold at a profit of 20%. If CP & SP each be less by 1000 there would be an increase in profit by 5/3%. Find CP of VCR?

    • akriti sood says:

      let c.p be x then sp =1.2x
      let new cp be x-1000 and new sp be 1.2x-1000 and new profit is 20+5/3 = 65/3%
      so,1.2x-1000=(100+65/3)/1000*(x-1000)
      from which x comes out to be 13000

  4. Shauqeen says:

    A man sells his product ata loss of 8%. If his SP is Rs.27600, what is his actual loss and his cost price?

  5. rajat srivastava says:

    On the basis of selling price of an article, the loss is calculated to be 2%. The percentage of loss on the basis of cost price is

  6. kapil gahatraz says:

    An article when sold at a profit of 5% yields Rs 15 more than when sold at a loss of 5%. Find The Cost Price?

    • k says:

      let cp=x so sp=1.05x for 5% profit
      sp=0.95x for 5% loss
      profit sp=loss sp + 15
      1.05x = 0.95x + 15
      so x = 150

  7. Babi says:

    A goes to nasik to buy an article costing 15%less than that in Bombay. He spends Rs. 150 on travelling and gains Rs. 150 after its sale in bombay. His profit % is.???

  8. kuldeep lagwal says:

    To compare the cost price , selling price, market price, profit, loss and discount % on eight articles purchase from the market?

  9. Radar says:

    A shopkeeper buys a thing at 10 % more and sells it at 10% less. Find hits profit percent

    • Aastha says:

      Lets say that he purchased at a price of 110, considering actual price of the thing is 100 rs.
      He sold it at a discount of 10%= 100×0.9= 90rs.
      So, He incurred a loss of 20 rs.
      Loss %tage= (20/110)*100=Approx. 20%

      else
      He sold it at a discount of 10%= 110×0.9= 99rs.
      Loss %tage= (11/110)*100=10%

  10. dipu says:

    The marked price of an article is 20 % more than it’s selling price. Find the rate of discount.

  11. mamtah says:

    What profit percent is made by selling an article at a certain price, if selling the same article by half of that price there would be a loss of 20%?

  12. Nikki says:

    If the CP of an article is decreased by 10%. How much should new CP be increased so that the profit remains same.

  13. komal says:

    30% profit on sp is what % on cp ?

  14. Shashi says:

    A man made a loss of 4% on an article he had sold for RS.240 more he had made a profit of 8% find the cost price of the article. Pls solve

    • shamera says:

      assume cost price as x
      c.p=100x
      s.p=1oo-4=96x,s.p=100+8=108x
      108x-96x=240
      12x=240
      x=240/12
      x=20
      therefore c.p=100*20
      c.p=2000

  15. dharmit says:

    A man sold his bicycle for Rs 810; losing one-ninth of its selling price, find:
    (i) The loss (ii) the cost price of the bicycle (iii) the loss percent

  16. Richa says:

    If an article is sold at 5% discount then he earns 25% profit. What profit will he earn if he gives no discount?

    • Aastha says:

      Consider the article has an original C.P= 100 Rs.
      for 25% Profit, S.P= 125
      Marked price= (S.P/ 95%)= approx 131 rs.

      Ofcourse, when no discount is given, the profit he earns is 31 rs. i.e. 6 Rs. more.

  17. sefat says:

    “A certain suits price was reduced by 25% in the first week and 20% in the next week . In the third week, the shop owner decided to offer additional 10% discount on the suit. What percent of the regular price was the final price of the suit after the two reductions?”

    • Aastha says:

      75%*80%=60%
      60% discount was offered at regular price. Which means Final Price = 60% discount on Regular.
      NOTE: this result is at the end of 2 reductions.

      60%*90%=54%
      54% discount is offered after 3rd reduction.

  18. nagendra says:

    A sum of Rs 40,000 annual simple interest rate of 10 percent at the end of 5 years the total amount is given. Rs 92 960 by the end of the 5th Vsn gives So tell your full repay the amount he had at the end of 2 years.

  19. Bianca917 says:

    the cost price of a book is $450 if the book is sold at a discount of 10%on its marked price then the profit per cent is 20%fin the marked price of the book

    • Aastha says:

      We Know, S.P= (1+profit%)*C.P
      hence, S.P= 1.2*450= 540 Rs.

      Also, 90% Marked Price= S.P
      Marked Price= 540/90% = 600

      Hence Marked Price= Rs. 600

  20. Prem Sagar says:

    3 frends go to an lodge there a servent takes rs30 for 1 night each gives rs10 but after some time the owener takes rs25 and tell his servent to retorne rs5, but he give backe rs1 for each and he keeps rs2,than 10-1 from each than rs9 than 9×3=27 and servent rs2 27+2=29 .Than were did rs1 gone

  21. Antim patidar says:

    If a person purchase two cows at a cost of rs 4200,then he sold one at a profit of 15% and other at a loss of 10%,but in this business he did not get any profit and loss…what will be the cost price of each cow?

    • Aastha says:

      Let’s Say the C.P1 of one cow= Rs. X
      Its, S.P1= (1.15*x) Rs.

      Also, C.P2 of the other cow= Rs. (4200-x) … as total C.P= Rs. 4200
      Its, S.P2= (0.9*(4200-x)) Rs.

      But, as NO Loss or Profit incurred.
      S.P1+ S.P2= C.P
      4830-1.15x+0.9x= 4200
      0.25x= 630
      x= (630/0.25)= 2520

      Hence, the C.P of 1st cow is Rs. 2520 and the 2nd cow is 1680 Rs.

  22. Umesh bisht says:

    Sp 770 profit 70

  23. Prix says:

    Find the selling price of the cost price is rs 1200 and loss percent is 25%

  24. Manaa says:

    Mr chowdhary purchased a house for Rs 6.1 lac and spent by Rs 30000 on its repairs.He then sold it for Rs 8 lac.Find his gain percentage??

    • Aastha says:

      Total Expenditure on the House= C.P= 6.1 Lac+30, 000= 6.4 lac
      S.P= 8 Lac
      Profit= S.P- C.P= 1.6 Lac
      Profit Percentage= (1.6Lac/6.4 Lac)*100= (1/4)*100= 25%

      Gain %tage= 25%

  25. Aarshna says:

    a man sold a camerafor rs2570 and made a loss of 180.?at what price did he purchase a camera?

  26. Madhavarao says:

    An electric item is sold at a profit of 16℅.if it were sold for 20rs more, there would have been a profit of 20℅.the cost price of the item is?

    • Aastha says:

      Say C.P of the electric item= Rs. x
      Hence, S.P = 1.16x

      Now, when S.P+20, profit is 20%
      Thus, 1.16x+20= 1.2x
      20= 0.04x
      x=500 Rs.
      Cost Price of the item is Rs. 500. And to gain 16%, S.P= 580 Rs. whereas for 20%= 580+20=600.. As suggested.

  27. Anil tanwar says:

    If a man buys a book for ₹36,which is available on 40% discount off the original price.what is the original price of the book?

    Please tell me

    • Aastha says:

      C.P for Man= 36 Rs.
      Price after discount of 40% is 36.
      Say the Marked Price= x
      x= 36/0.6= 60Rs.
      The original Price of the book is 60 Rs.

  28. Abhay kumar says:

    PlSe solve this if c.p of an item is 115 and s.p is 120 then find gain% and Ans is 12 1/2

  29. anil says:

    a man sells a car to his friend at a loss of 2.5% who again sells it for Rs 40950 making a profit of 5% what was initial value of the car

  30. rahul says:

    a person sells 15 things in 30 Rs and earn 10% profit. if he sells similar 10 things in Rs 25, then what will be his percentage loss or gain ?

    • shrashti says:

      SP is rs 30 & p% is 10%
      Thus, CP= 30X100/110 = 300/11
      Now, SP is rs 25
      So, P= SP-CP=300/11 – 25=25/11
      P%=25/11 X 11/300 X100 = 25/3%

  31. baba says:

    An article is sold at a discount of 5% on the list price. If no discount was given on the list price the profit would have been 20%. What is the profit percent in transaction? Please solve it.

    • Aastha says:

      Say C.P originally of the Article is Rs. 100
      To achieve a profit of 20% , List Price= Rs. 120
      Now, 95% of List Price= S.P.
      Hence, S.P= 120*0.95= 114 Rs.

      Profit Percentage in transaction= (14/100)*100= 14%

  32. shrashti says:

    An article is marked 17% above its CP. The profit gets increased by Rs288, when SP of this article is increased by 20%. If the marked price of the article is Rs1404, what is the original SP of the article?

  33. kranthi kumar says:

    a shopkeeper prints the price of coat 25% above the cost price.he gives 10% discount on listed price.for person who pays tax immediately gives a additional discount of 4% on the reduced price. what is profit percentage?

  34. Sushma says:

    The Formula is CP- (more gain/diff in %’s)*100

    Answer is 100

  35. Anil says:

    By selling 33 books, a shopkeeper get profit equals to cost price of 11 books. Find his profit/loss%?

    • Aastha says:

      Say C.P of 1 book= 1 Re.
      C.P of 11 books= Rs. 11 and similarly C.P of 33 books= rs. 33
      Now, Profit= S.P- C.P
      =x-33= 11
      S.P of 33 books= 44 Rs.
      Profit %tage= (11/33)*100= 1/3%

  36. arindam says:

    Rohit marks his goods at 40% above the cost price but allows a discount of 5% for cash payment to his customers.what actual profit does he make if he receives Rs 1064 after allowing the discount
    pl solve this problem

    • Aastha says:

      Here, Rohit Sold his goods at a final price of 1064, i.e S.P
      Now, 95% of Marked Price= S.P
      Marked Price= (S.P/0.95)= 1064/0.95= Rs. 1120.
      Now, For customer, 1120 Rs. was the actual seen Price over which 5% discount was offered.
      Given that Marked Price= 40% more than C.P
      Hence, C.P= 1120/1.4= 800Rs.

      Profit= (264/800)*100= 33%

  37. dilip says:

    10 मोमबत्ती को बेचने पर 1 आदमी 3 पेनो के बिकय मूलय के बराबर लाभ कमाता है आैर 10 पेन को वेचने पर उसे 4 मोमबती के विकय मूल के वरावर हाानि होती है लाभ पतिशत आैर हाानि पतिशत का सखया मान सामान है मोमवती का कय मूलय पेन के कय मूलय का आधा हो तब मोमबती तथा pen के विकय मूलय का अनुपात ज्ञात किजिय

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