Tips and Tricks for Profit & Loss

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Important Terms in Profit and Loss


SP – Selling price

CP – Cost price

MP – Marked price


Formulas

  1. Profit = SP – CP
  2. Loss = CP – SP
  3. Profit% = {(SP – CP)/CP} * 100
  4. Loss% = {(CP – SP)/CP} * 100
  5. SP = (1+ profit%) * CP
  6. SP = (1 – Loss%) * CP
  7. CP = SP/(1+profit%)
  8. CP = SP/(1-Loss%)
  9. MP = SP+ Discount
  10. MP = SP/(1-Disount%)
  11. Discount% = {(MP – SP) / MP} * 100
  12. Profit% = MP% – Discount% – (MP% * discount%)
  13. If profit and loss are same(x), then loss%= (X/10)2

Problem

(1) A person incurs 5% loss by selling a watch for Rs.1140 at what price should the watch be sold is earn 5% profit?

Solution: CP = SP/(1-Loss%)

CP = 1140*100/(100-5)

CP = 1200

To incur 5% profit the product should be sold = 1200*105/100

SP = 1260

(2) An article sold at a loss of 10%, Its CP is 800. A discount of 20% was offered on the labeled price while selling. What is the loss% at the labeled price?

Solution: SP = (1- loss%)*CP

SP = 800*90/100 = 720

MP = SP/(1-Disount%)

MP = 720/(1-20%) = (720*100)/80 = 900

Loss % at labeled price = ((MP-SP)/MP)*100

Loss% = ((900-720)/900)*100 = 20%

(3) By what percent must the cost price be raised in fixing the sale price in order that there may be a profit of 20% after allowing a commission of 10%.

Solution: Usual method: CP =100 rs , profit = 20%

SP = 120 rs

Commission 10%, then MP = SP/(1-discount%)

MP = 120/(1-10%) = 120/(1-(10/100))

=120* 100/(100-10)

= 133.3 Rs

MP% = ((MP- CP)/CP)*100

=33.3%

So MP should be 33.3% more than CP to get 20% profit after allowing commission of 10%

          Shortcut :

Profit%= MP% – Discount% – (MP%*discount%)

Let MP%=x%

20/100 = x/100 – 10/100 – ((x/100)*(10/100))

30/100 = 90x/10000

X = 33.3%

(4) The price of land came to a person through three middle man each gaining 20% if the person purchased the land for RS.3,45,600 the original cost of land was ?

Solution : CP = SP/(1+profit%)

CP =  345600*(100/120)*(100/120)*(100/120)

CP = 2,00,000 rs

(5) A cloth merchant sold half of his cloth at 20% profit and half of the remaining cloth at 20% loss and remaining at the cost price. In total transmission what will be his gain or loss?

Solution: Let CP = 100

Half of the cloth at 20% profit, SP = 50 *120/100 = 60

Half of the remaing cloth at 20% loss, SP = 25 *80/100 = 20

Reaming cloth at CP, Therefore SP = 25

On total transaction SP = 60 + 20 +25 = 105

Profit% = 5%


Solve Yourself and Comment the answer

Question 1: An article is sold at a loss of 10%. Had it been sold for Rs. 9 more, there would have been a gain of 25/2% on it. The cost price of the article is :
(a) Rs. 40
(b) Rs. 45
(c) Rs. 50
(d) Rs. 35

Question 2: A man sold an article at a loss of 20%. If he has sold that article for Rs. 12 more he would have gained 10%. Find the cost price of that article :
(a) Rs. 60
(b) Rs. 40
(c) Rs. 30
(d) Rs. 22

Question 3: If an article is sold for Rs. 178 at a loss of 11%, what should be its selling price in order to earn a profit of 11%?
(a) Rs. 222.50
(b) Rs. 267
(c) Rs. 222
(d) Rs. 220

Question 4: A businessman sells a commodity at 10% profit. If he had bought it at 10% less and sold it for Rs. 2 less, then he would have gained 50/3%. The cost price of the commodity is
(a) Rs. 32
(b) Rs. 36
(c) Rs. 40
(d) Rs. 48

Question 5:A car worth Rs. 1,50,000 was sold by X to Y at 5% profit. Y sold the car back to X at 2% loss. In the entire transaction.
(a) X gained Rs. 4,350
(b) Y lost Rs. 4,350
(c) X gained Rs. 3,150
(d) X lost Rs. 3,150

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