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: How your student experience could be messed up affected by Corona.

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.


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%.


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?


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.


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?


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.


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?


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.


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.


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



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



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



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.

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

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  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
        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

      • Sendhil Kumar S K says:

        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/-

    • 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

    • Pankaj pandey says:

      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

      In second case,



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


      Thus, The Selling price is Rs. 270.

    • Priya says:

      a man sells three articles one at a loss of 10% another at a profit of 20% and third at a loss of 25% if selling price of all three same then find how much % is their average cp lower than or higher average their cp

    • Anushka says:

      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.

  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.


      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

      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?

  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. 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%

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

  9. komal says:

    30% profit on sp is what % on cp ?

  10. 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
      therefore c.p=100*20

  11. 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

    • Aastha says:

      S.P= 810 Rs.
      S.P+Loss= C.P
      Loss=(1/9)*S.P= 90 Rs.
      hence, C.P= 900 Rs.
      Loss %tage= (90/900)*100= 10%

  12. 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.

  13. 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:

      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.

      54% discount is offered after 3rd reduction.

  14. 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

    • Oyewale Adedunmola says:

      Please is it every question that those formulas can be applied and please how do i break it down to know which formula to use

  15. 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.

  16. 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%

  17. Aarshna says:

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

  18. 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.

  19. 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.

  20. 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

  21. 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

  22. 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%

  23. 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%

  24. 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%

  25. 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%

      • Shubham says:

        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

    • manas says:

      suppose c.p=100rs
      so m.p = 100+(100*40%)=140
      s.p = 140-(140*5%) =133
      he got 133 rs on 100 rs cost price his profit% = 100*(33/100)=33% profit he got
      now 133 = 1064
      100=1064*100/133 = 800
      c.p = 800
      profit = 1064-800= rs264 (Answer )

  26. 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

  27. Digvijaysinh says:

    A shopkeeper sells 25 pens 10% for a profit of 45 rupees and 50% profit. Fetch. What percentage of profit is there if it does not provide returns ?.

  28. Ayush sharma says:

    a trader buys goods and increase its selling price by 50%. He then offers a 20% discount and makes a profit of ₹500. the initial cost of the goods was

  29. Naveen says:

    sum of cost price of article was 12000. first article will sold at 15% gain and other article will sold at 12% loss.the overall loss occured on whole is 90.what is cost price of first article

  30. Sudeep says:

    100 goods are purchase at the rate of rs 240. 1/4 of the Goods are sold at the gain of 10%. At what percentage profit should the remaining good should be sold so that profit on the whole outlay becomes 25%.

  31. owido says:

    hadija would make a profit if she sells her mobile phone for 4800.and would make a loss if she sells it 2880.if the profit is five times the loss.calculate the mark price of the phone.

  32. sushil hamal says:

    The item is worth 90% of its original price. If you add 90 roubles to the price with the discount, the price will be equal to original. What is the initial price of the item?

  33. Adeyemi Deborah. says:

    Please I have a question can you help me with the question. If a trader bought a radio 36 naira and sold it for 45 naira
    Express the profit as a percentage of the cost price.

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