APTITUDE-Problems on Profit and Loss

Profit and Loss

Important Facts:

Cost Price: The price at which an article is purchased,
is called its cost price,abbreviated as C.P.

Selling Price: The price at which an article is sold,
is called its selling price,abbreviated as S.P.

Profit or Gain: If S.P. Is greater than C.P. The seller
is said to have a profit or gain.

Loss:if S.P. Is less than C.P., the seller is said to
have incurred a loss.

Formulae

1.Gain=(S.P-C.P)
2.Loss=(C.P-S.P)
3.Loss or Gain is always reckoned on C.P.
4.Gain%=(gain*100)/C.P
5.Loss%=(loss*100)/C.P
6.S.P=[(100+gain%)/100]*C.P
7.S.P=[(100-loss%)/100]*C.P
8.C.P=(100*S.P)/(100+gain%)
9.C.P=(100*S.P)/(100-loss%)
10.If an article is sold at a gain of say,35%,then S.P=135% of C.P.
11.If an article is sold at a loss of say,35%,then S.P=65% of C.P.
12.When a person sells two similar items, one at a gain of say,x%,and the other at a loss of x%,then the seller always incurs a loss given by Loss%=[common loss and gain %/10]2=(x/10)2.
13.If a trader professes to sell his goods at cost price,but uses false weight,then Gain%=[(error/(true value-error))*100]%.
14.Net selling price=Marked price-Discount.

Simple Problems

1.A man buys an article for Rs.27.50 and sells it for Rs.28.60
Find the gain percent.

Sol: C.P=Rs 27.50 S.P=Rs 28.60
then Gain=S.P-C.P=28.60-27.50=Rs 1.10
Gain%=(gain*100)/C.P% =(1.10*100)/27.50%=4%

2.If a radio is purchased for Rs 490 and sold for Rs 465.50 Find the loss%?
Sol: C.P=Rs 490 S.P=Rs 465.50
Loss=C.P-S.P=490-465.50=Rs 24.50
Loss%=(loss*100)/C.P% =(24.50*100)/490%=5%

3.Find S.P when C.P=Rs 56.25 and Gain=20%
Sol: S.P=[(100+gain%)/100]*C.P
S.P=[(100+20)/100]56.25=Rs 67.50

4.Find S.P when C.P=Rs 80.40,loss=5%
Sol: S.P=[(100-loss%)/100]*C.P
S.P=[(100-5)/100]*80.40=Rs 68.34

5.Find C.P when S.P=Rs 40.60,gain=16%?
Sol: C.P=(100*S.P)/(100+gain%)
C.P=(100*40.60)/(100+16)=Rs 35

6.Find C.P when S.P=Rs 51.70 ,loss=12%?
Sol: C.P=(100*S.P)/(100-loss%)
C.P=(100*51.70)/(100-12)=Rs 58.75

7.A person incurs 5% loss by selling a watch for Rs 1140 . At what price should the watch be sold to earn 5% profit?
Sol: Let the new S.P be Rs x then,
(100-loss%):(1st S.P)=(100+gain%):(2nd S.P)
(100-5)/1140=(100+5)/x
x=(105*1140)/95=Rs 1260

8.If the cost price is 96% of the selling price,then what is the profit percent?
Sol: let S.P=Rs 100 then C.P=Rs 96
profit=S.P-C.P=100-96=Rs 4
profit%=(profit*C.P)/100%
=(4*96)/100=4.17%

9.A discount dealer professes to sell his goods at cost price but uses a weight of 960 gms for a Kg weight .Find his gain %?

Sol: Gain%=[(error*100)/(true value-error)]%
=[(40*100)/1000-40)]%=25/6%

10.A man sold two flats for Rs 675,958 each .On one he gains
16% while on the other he losses 16%.How much does he gain or
lose in the whole transaction?

Sol: loss%=[common loss or gain%/10]2=(16/10)2=2.56%

11.A man sold two cows at Rs 1995 each. On one he lost 10% and
on the other he gained 10%.what his gain or loss percent?

Sol: If loss% and gain% is equal to 10 then there is no loss or no gain.

12.The price of an article is reduced by 25% in order to restore the must be increased by ?

Sol: [x/(100-x)]*100 =[25/(100-25)]*100
=(25/75)*100=100/3%

13.Two discounts of 40% and 20% equal to a single discount of?
Sol: {[(100-40)/100]*[(100-20)/100]}%=(60*80)/(100*100)%
=48%
single discount is equal to (100-48)%=52%

Difficult Problems

1.The cost of an article including the sales tax is Rs 616.The rate of sales tax is 10%,if the shopkeeper has made a profit of 12%,then the cost price of the article is?
Sol: 110% of S.P=616
S.P=(616*100)/110=Rs 560
C.P=(100*S.P)/(100+gain%)
C.P. =(100*560)/(100+12)=Rs 500

2.Sam purchased 20 dozens of toys at the rate of 375 Rs per dozen.He sold each one of then at the rate of Rs 33.What was his
percentage profit?

Sol: C.P of one toy=Rs 375/12=Rs 31.25
S.P of one toy=Rs 33
profit=S.P-C.P=33-31.25=Rs 1.75
profit %=(profit/C.P)*100
=(1.75/31.25)*100
profit% =5.6%

3.Two third of consignment was sold at a profit of 5% and the
remainder at a loss of 2%.If the total was Rs 400,the value of the
consignment was?

Sol: let the total value be Rs x
value of 2/3=2x/3, value of 1/3=x/3
total S.P value be Rs x
total S.P=[(105% of 2x/3)+(98% of x/3)]
=(105*2x)/(100*3)+(98/100)+x/3
=308x/300
(308x/300)-x=400
8x/300=400
x=(300*400)/8=Rs 15000

4.Kunal bought a suitcase with 15% discount on the labelled price. He sold the suitcase for Rs 2880 with 20% profit on the labelled
price .At what price did he buy the suitcase?

Sol: let the labelled price be Rs x
then 120% of x=2880
x=(2880*100)/120=Rs 2400
C.P=85% of the 2400
(85*2400)/100=Rs 2040

5.A tradesman gives 4% discount on the marked price and gives
article free for buying every 15 articles and thus gains 35%. The
marked price is above the cost price by

Sol: let the C.P of each article be Rs 100
then C.P of 16 articles=Rs (100*16)=Rs 1600
S.P of 15 articles =1600*(135/100)=Rs 2160
S.P of each article =2160/15=Rs 144
If S.P is Rs 96, marked price =Rs 100
If S.P is Rs 144,marked price =(100/96)*144=Rs 15000
therefore marked price=50% above C.P

6.By selling 33m of cloth ,one gains the selling price of 11m.Find
the gain percent?

Sol: gain=S.P of 33m-C.P of 33m
=11m of S.P
S.P of 22m=C.P of 33m
let C.P of each meter be Rs 1,then C.P of 22m=Rs 22
S.P of 22m=Rs 33
gain=S.P-C.P=33-22=Rs 11
gain%=(gain/C.P)*100
=(11/22)*100=50%

7.The price of a jewel, passing through three hands, rises on the whole by 65%.if the first and second sellers earned 20% and 25%
profit respectively,find the percentage profit earned by the
third seller?

Sol: let the original price of the jewel be Rs P and
let the profit earned by the third seller be x%
then (100+x)% of 125% of P=165% of P
[(100+x)/100]*(125/100)*(120/100)*P=(165/100)*P
100+x=(165*100*100)/(125*120)
100+x=110
x=10%

8.When a producer allows 36% commission on the retail price of his product ,he earns a profit of 8.8%.what would be his profit
percent if the commission is reduced by 24%

Sol: let retail price =Rs 100
commission=Rs 36
S.P=retail price-commission=100-36=Rs 64
But profit=8.8%
C.P=(100*C.P)/(gain+100)=(100*64)/(100+8.8)=Rs 1000/17
new commission=Rs 12
new S.P=100-12=Rs 88
gain=88-(1000/17)=Rs 496/17
gain%=gain*100/C.P
=(496*17*100)(17*1000)
gain%=49.6%

9.Vikas bought paper sheets for Rs 7200 and spent Rs 200 on
transport. Paying Rs 600,he had 330 boxes made,which he sold
at Rs 28 each. His profit percentage is

Sol: total investments=7200+200+600=Rs 8000
total receipt=330*28=Rs 9240
gain=S.P-C.P
=total receipt-total investments
gain=9240-8000=Rs 1240
gain% =gain*100/C.P=1240*100/8000=15.5%

10.A person earns 15% on investment but loses 10% on another investment .If the ratio of the two investments be 3:5 ,what is the gain or loss on the two investments taken together?

Sol: let the investments be 3x and 5x
then total investment=8x
total receipt=115% of 3x+90% of 5x
=115*3x/100+90*5x/100=7.95x
loss=C.P-S.P=8x-7.95x=0.05x
loss%=.05x*100/8x=0.625%

11.The profit earned by selling an article for Rs 900 is double the loss incurred when the same article is sold for Rs 490 .At what
price should the article be sold to make 25% profit?

Sol: let C.P be Rs x
900-x=2(x-450)
3x=1800
x=Rs 600
C.P=Rs 600 , gain required=25%
S.P=(100+gain%)*C.P/100
S.P=(100+25)*600/100=Rs 750

12.If an article is sold at 5% gain instead of 5% loss,the seller
gets Rs 6.72 more. The C.P of the article is?

Sol: let C.P be Rs x
105% of x-95% of x=6.72
(105/100)*x-(95/100)*x=6.72
x/10=6.72
x=Rs 67.21.

If you have questions, please ask below

54 Comments


  1. marina says:

    please make the solution of each problems little more clear and descriptive

  2. Manikandan says:

    it s awesome, sample problems and answers are good

  3. priya paraswani says:

    a person sold a tv at a gain of 5%.Had he bought it for 5 % less and sold it for rs 17.50 less hw would have made a profit of 10%.Find the cost price of the TV set.

    • shahina says:

      Ans for the above ques !!

      Assume CP as x,
      1st SP = 105% of x = (105/100)x = 21x/20
      2nd SP = 95% of x = (95/100)x = 19x/20
      2nd SP = 110% of (19/20)x = ((110/100) / (19x/20) = 209x/200
      Therefore,
      (21x/20)-(209x/200)=17.50
      x/200 = 17.50
      x = 17.50 x 200
      x = 3500
      Hence, CP = Rs.3500
      Is it right ??

  4. Anurag Soni says:

    i got very nice collections of the apptitude question from this site…

  5. Lala says:

    20% more can be gained if a piece of cloth is sold for Rs. 46.50 instead of Rs. 39. Find the cost price.

    • sagar lama says:

      LET C.P
      .=RS30/-
      THEN FOR 1ST S.P. WE GET PROFIT%=(9/30)*100=30%
      NOW FOR 2ND S.P. WE GET PROFIT%=55%
      SO,WE GET WHEN THE PROFIT% DIFFERENCE=25% C.P.=RS30
      SO WHEN PROFIT% DIFFERENCE=20% C.P.=RS (30/25)*20=RS24/-ONLY

      • sagar lama says:

        THAT CONCEPTS OF SOLVING THE ABOVE GIVEN PROBLEMS IS ABSOLUTELY WRONG……I AM VERY VERY SORRY FOR GIVING THE WRONG SOLUTION……..

    • sagar lama says:

      LET C.P.=RSX/-
      FIRSTLY LET US CONSIDER Y% PROFIT AT S.P. OF RS39/-
      THEN IT IS OBVIOUS THAT HE GET (120+Y)% PROFIT AT S.P.OF RS46.50/-
      NOW WE CAN WRITE FOR THE FIRST PART S.P.={(100+Y)/100}*X=39
      AND FOR THE SECOND PART S.P.={(120+Y)/100}*X=46.50
      SO AFTER CALCULATION WE GET THE VALUE OF X AS RS37.50/-
      SO, THE COST PRICE OF AN ARTICLE=RS37.50/-ONLY…………I THINK YOU GOT IT……..IF NOT YOU ARE MOST WELCOME TO ASK ANY KIND OF DOUBT REGARDING THE QUANTITATIVE APTITUDE PROBLEMS……………

    • disha says:

      46.50-39= 7.5
      20% = 7.5
      100 % = (7.5/20)* 100
      = 37.5 is the cp

  6. husameldin says:

    thanx 4 the great help,i appreciate zat.
    bt in the last prblem,why u ve written 105%of x-95%of x=67.21 i cant get it.
    specially x-95%.
    thanx

    • sagar lama says:

      the meaning of the expression given above states that when the seller sells the articles at a price by Rs6.72/- more than the previous selling price which he was giving he gets a profit of Rs6.72/-

  7. Suresh Kumar says:

    The Cost Price of an article is 96% of the Selling Price then the Profit Percentage is ?

  8. deepak kumar says:

    if an article is sold at 8% profit instead of 8% loss , it would have brought rs 12 more . find out the cost priceof the articale . what is the solution ?

    • sagar lama says:

      let c.p.=x
      1st s.p.=108x/100 & 2nd s.p.=92x/100
      now a.t.q.we can write as follows
      (92x/100)+12=(108x/100)
      16x/100=12
      therefore c.p.of the article=Rs.75/-only

    • arijit says:

      according to question
      (8+8)% = 12
      or, 16% = 12
      or, 100% = 12*100/16 = 75
      cost price of the article is 75

  9. deepak kumar says:

    compound interest on a sum for 2 year at 4% per annum is Rs 102 . the simple interest on the same sum for the same period at the same rate will be

    • sagar lama says:

      We know Amount=Principal+Interest
      In short,A=P+(PRT)/100
      A=P(1+RT/100)
      NOW BY SUBSTITUTING THE GIVEN VALUES WE GET
      PRINCIPAL=RS.94.4/-
      SO,SIMPLE INTEREST=94.4*4*2=RS.755.20/-ONLY

      • sagar lama says:

        THE ANSWER GIVEN ABOVE SHOULD BE DIVIDED BY 100…..
        And moreover we also know that simple interest is always less than compound interest interest on a same sum,same rate and same period of time…..
        in the solution given above i forgot to divide by 100
        so its your duty to correct the answers given above

      • sagar lama says:

        i am very very sorry for the wrong answer as i did not read the questions nicely since i took 102as the amount which is not so it should have been taken as the interest as given in the question above……….
        please kindly take note of it

    • sagar lama says:

      FIRSTLY THROUGH THE HELP OF THE COMPOUND INTEREST GIVEN IN THE QUESTION, WE GET THE PRINCIPAL=RS1250/\
      THEREFORE SIMPLE INTEREST=(1250*4*2)/100=RS100/-
      I THINK YOU GOT IT………

  10. sagar lama says:

    if anymore doubt regarding any questions based on quantitative aptitude,you are most welcome toask the question very freely as per my email-id is given below

  11. rishab says:

    the ans for question no. 4 is wrong !!
    it should be 76.38

  12. sagar lama says:

    friends please make carefully note of it that the process of solving the questions no.7 of the difficult problems as given above is absolutely wrong………..

  13. sachin says:

    A vendor lemons at 6 for a rs. how many for a rupee must be sell to gain 20%?

  14. N.Surendiran says:

    I need an answer for this question!

    Amal bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more than what Amal had paid. What % of the total amount paid by Amal was paid for pens?

    a) 37.5% b) 62.5% c) 50% d) None of these

  15. N.Surendiran says:

    Amal bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more than what Amal had paid. What % of the total amount paid by Amal was paid for pens?

    a) 37.5% b) 62.5% c) 50% d) None of these

    i need an answer Please?

  16. N.Surendiran says:

    Amal bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more than what Amal had paid. What % of the total amount paid by Amal was paid for pens?

    a) 37.5% b) 62.5% c) 50% d) None of these

    i need an answer Please?

  17. N.Surendiran says:

    Amal bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more than what Amal had paid. What % of the total amount paid by Amal was paid for pens?

    a) 37.5% b) 62.5% c) 50% d) None of these

    i need an answer Please?

  18. profit and loss says:

    A man purchased some eggs at 3 for Rs. 5 and sold them at 5 for Rs12. he gained Rs.143 in the whole transaction . How many eggs did he purchase?
    i need answer these

  19. profit and loss says:

    A Sum of money was distributed between A and B . A got 60% of all the money and B got Rs. 1170 less than A . how much money was distributed between A ans B.

  20. prabhu says:

    . In a shop 80% of the articles are sold at a profit of 10% and the remaining at a loss of 40%.what is the overall profit/loss?
    a.10% profit b.10% loss c.15% profit d. no profit, no loss

  21. sagar says:

    a man bought a horse and a carriage for rs.3000 he sold the horse at a gain of 20% and the carriage at a loss of 10% there by he gain 2% on the hole find the cost of horse…
    anybody plz help me to solve this problem..

  22. Manas Ranjan Mohapatra says:

    If a man sold a product in 10rs loss,another man sold same product in 20%profit.find the actual price of that product.

  23. onescell says:

    I got a very nce and clear problems.I mean, i was able to share it with some of my friends…………

  24. onescell says:

    I got a very nice and clear problems.I mean, i was able to share it with some of my friends…………

  25. rani says:

    one sold some balls 450rs.and 15rs less for each ball.5 balls added for this remaining money.then how much forst he sold.

  26. sunil dutta says:

    plz give me 10 ums where marked price(m.p),sales Tax% , is given and we have to find selling price . it is very urgent. I needed ……….

  27. vinit says:

    A man sells two tables for $1200 each; one at a profit of 10% and other at a loss of 10%. Find the actual gain or loss.

  28. vinit says:

    A watch passes through three hands and every one makes a gain of 25% and the third sold it for $250. What did the first pay for it?

  29. Anusha says:

    Wasim started a business with Rs 25000 and after 4 months Ali joined him with Rs 60000. Wasim received Rs 58000 including 10% of the profits as commission for managing the business. What amount Ali will get?

  30. shalini says:

    25/4% gain fretches a profit of Rs.50 on a article. then find c.p of article?

  31. sravan says:

    a person sold an article on 25% discount he gained 25% profit. if he sold it to 10% discount then what is the profit %?

  32. Susant says:

    During a sale a dealer reducd his goods 25% below the mark price which has been originally been fixed at 20% profit on cost after allowing 10% trade discount.what % did he gain or lose?

  33. ananth setty says:

    john buys a telephone handset for rs600 from kolkata and sells it at ranchi at a gain of 25%.if his overhead expenses are 5%of the selling price,then he sold the telephone handset for
    (a)rs 1000 (b)rs 780 (c)rs 750 (d)rs 800 (e)rs 720

  34. ananth setty says:

    anybody try this out quickly plz

  35. PREET says:

    A SELLS HIS GOODS AT 15% DISCOUNT. FIND THE PRICE OF THE ARTICLE WHICH IS SOLD FOR RS.680/-

  36. netra says:

    A man bought 2 cows for Rs.1040. He sold one at a loss of 15% and the other at a profit of 36% and then he found that each cow was sold for the same price. Find the cost price of each cow.

  37. komal says:

    A merchant earns 25% profit in general. Once his 25% consignment was abducted forever by some goondas . trying to compensate his loss he sold the rest amount by increasing his selling price by 20%. what is the new percentage profit or loss?

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