Important Terms in Profit and Loss

**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%

**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