Profit and loss Formulas Problems and Tricks

Profit and loss problems involves various terms like cost price, selling price, marked price etc. Basically, it is a difference between selling price and cost price. Cost price is the price paid to purchase an article or a product or we can say it is a cost incurred in manufacturing an article. Selling price is the price at which a product is sold.

Must read
Quantitative Aptitude series
Guide to Quantitative aptitude

Various profit and loss formulas used in profit and loss:


1) Generally, profit is calculated as:
                   Profit or gain = Selling price(S.P) - Cost price(C.P)
2) Similarly, Loss = Cost price - Selling price
3) Gain percentage(%) = Gain * 100
                                     C.P.
4) Loss percentage(%) = Loss * 100
                                     C.P.
5) There is a direct relationship between selling price and cost price:
                    S.P. = 100 + Gain percentage * C.P. (In case of gain)
                                         100
                    S.P. = 100 - Loss percentage * C.P. (In case of loss)
                                         100


For Example :

If an article is sold at gain of 27%, then by using first formula , you can find that S.P. is 127% of C.P.
Similarly, If an article is sold at loss of 18%, then by using second formula , you can find that S.P. is 82% of C.P.

6) If a person sells two commodities at same prices. On one he gains x% and loses x% on another, then as a whole he will be in loss and the loss percentage will be equal to:
       (Common gain or loss percentage)^2  = x^2
                           100                                 10

Note: Here is an example to find gain in case of dishonesty.
Problem 1: A dishonest dealer professes to sell his goods at cost price but he uses a weigh 960 grams for 1 kg. How too calculate gain percentage?

Solution: Gain percentage =          Error            * 100 = 40  * 100 (Ans in %)
                                         True value - Error              960

25 comments:

  1. By selling a watch for Rs. 144 a man

    loses 10%. At what price should he sell it in

    order to gain 10%?

    Its in percentage(Profit and loss) notes solved example 2
    i got till CP =160rs but then its written Gain required =15% and final answer as Rs 184..plz expailn

    ReplyDelete
    Replies
    1. SP with CP as Rs.100 = 90 as there is 10 % loss
      New SP with CP as Rs.100 = 115 as he needs 15% gain
      SP with CP as Rs.100 : actual SP =New SP with CP as Rs.100 : New SP
      90 : 144 = 115 : x
      90 x = 114 * 115
      x = 184

      Delete
    2. 90x=144*110
      x=15840/90
      x=176

      Delete
  2. You are correct Vikku.

    ReplyDelete
  3. @vikku Ahhh sorry for that, it was 18% instead of 27%. Thanks for correction :)

    ReplyDelete
  4. If an article is sold at gain of 27%, then by using first formula , you can find that S.P. is 127% of C.P.
    Similarly, If an article is sold at loss of 27%, then by using second formula , you can find that S.P. is 82% of C.P.



    in the first case .
    gain % -

    (100+27) * 100
    -------------------- = 127 % Answer
    100

    and in loss case

    (100-27) * 100
    ------------------ = 73 % loss answer
    100

    Then why are you showing 82 % in loss case ??

    Please correct me

    ReplyDelete
    Replies
    1. Here we are calculating profit or loss on the basis of cost price.

      Delete
    2. hey...! Vikku.... 100-27 or 100-18 once check it

      Delete
  5. A shop keeper sold a hat at 12% profit. Had he sold it for rs.24 more he would have gained 18%, what is the cost price of the hat? plz may i know thw solution,,,

    ReplyDelete
    Replies
    1. SP1= 1.12 CP
      SP2-= SP1+ 24= 1.12CP + 24= 1.18CP

      Since, 1.12CP + 24 = 1.18CP,
      Multiplying both sides by 100, we get-> 112CP + 2400= 118CP
      Hence, CP= 2400/6 = 400

      Answer is: CP=400.

      Delete
  6. A Shop keeper sold a hat at 12% profit. had he sold it for rs.24 more he would have gained 18%, what is the cost price of the hat?

    ReplyDelete
    Replies
    1. 18%-12%= 4%
      so 4% of X = 24
      x= 400

      Delete
  7. a fruit vendor buys 120 shimla apples at 4 for rs100 and 120 golden apples at 6 for rs100. she decides to mix them and sells at 10 for 200.she will make gain or loss?

    ReplyDelete
  8. fruit vendor will get 5 rs of loss

    ReplyDelete
    Replies
    1. how he wl get only 5 rs loss
      120 shimla apple means 120/4= 30 sets each of 100= 30*100= 3000 rs shimla apple
      similarly 120 golden apple means 120/6= 20 sets each of 100= 2000 rs of golden apple
      now toatal appls are 120=120=240 means 240/10= 24 sets & s.p. of one set is 200 means total sp is 200*24= 4800
      coast price was 3000+2000=5000 so the loss is 5000-4800=200

      Delete
  9. A shopkeeppeer purchesed 5char and 7 tables per 5850. On tables he gets 16% profit and on chair 10% profit finally he received 711 as profit find the cost price of tables and chair?

    ReplyDelete
  10. 18% - 12%= 6 %
    6%= 24
    1% = 4

    100% = 400
    i.e CP = 400

    ReplyDelete
  11. sir any shortcuts for Simple &Compound interests??

    ReplyDelete
  12. please,,, any1 give me d explaination for d question,,,,, if profit earned after selling an article for 1516 rs is d same as loss incured after selling the article for rs 1492, what is cost prize of the article???????

    ReplyDelete
  13. By selling a watch for Rs 1440, a man losses 10%. At what price should he sell it to gain 5 %

    ReplyDelete

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