# Profit and Loss

**Important Terms**

SP – Selling price

CP – Cost price

MP – Marked price

**Formulas**

Profit = SP – CP

Loss = CP – SP

Profit% = ((SP – CP)/CP) * 100

Loss% = ((CP – SP)/CP) * 100

SP = (1+ profit%) * CP

SP = (1 – Loss%) * CP

CP = SP/(1+profit%)

CP = SP/(1-Loss%)

MP = SP+ Discount

MP = SP/(1-Disount%)

Discount% = ((MP – SP) / MP) * 100

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

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%