# Profit and Loss

Business transactions have now-a-days become common feature of life. When a person deals in the purchase and sale of any item, he either gains or loses some amount. The aim of any business is to earn profit.

Cost Price (CP): The cost price of an article is the price at which an article has been purchased.

Selling Price (SP): he selling price of an article is the price at which an article has been sold.

Profit or Gain: If the selling price of an article is more than the cost price, there is a gain or profit.

Profit = SP - CP

Loss: If the cost price of an article is greater than the selling price, the seller suffers a loss.

Loss = CP - SP

Marked Price (MP): Price printed on the product for sale. If seller gives any discount, selling price will be different from the marked price.

Profit % = Profit/CP × 100

Loss % = Loss/CP × 100

Cost Price

If SP and Profit % is given, then CP = 100/(100 + Profit %) × SP

If SP and Loss % is given, then CP = 100/(100 - Loss %) × SP

Discount = MP - SP

Discount % = Discount/MP × 100%

### Examples

Example 1: Anu bought a necklace for Rs. 750 and sold it for Rs. 675. Find her percentage loss

CP = 750, SP = 675

Loss = CP – SP = 750 – 675 = 75

Loss % = 75/675 × 100

= 10%

Example 2: Mr. Sharma buys a cooler for Rs. 4500. For how much should he sell so that there is a gain of 8%?

CP = 4500, Gain % = 8%

Gain = 8% of 4500 = 360

SP = CP + Profit = 4500 + 360

= Rs. 4860

Example 3: By selling a fridge for Rs. 7200, Pankaj loses 10%. Find the cost price of the fridge?

SP = 7200, Loss % = 10%

CP = SP + Loss

Loss % = Loss/CP × 100

Loss % = (CP - SP)/CP × 100

10 × CP = (CP - SP) × 100

90 × CP = 100 × SP

CP = 100/90 × 7200

= Rs. 8000

Example 4: A fruit seller buys apples at the rate of Rs. 12 per dozen and sells them at the rate of 15 for Rs. 12. Find his percentage gain or loss?

SP of 15 apples = 12

SP of 12 apples = 12/15 × 12 = 9.6

CP of 12 apples = 12

Loss = 12 - 9.6 = 2.4

Loss % = 2.4/12 × 100

= 20%

Example 5: A shopkeeper professes to sell his goods on cost price but uses 800 gm, instead of 1 kg. What is his gain %?

Here, cost price of 1000 gm is equal to selling price of 800 gm

Profit = 1000 - 800 = 200

Profit % = 200/800 × 100

= 25%

Example 6: If the selling price of 12 articles is equal to the cost price of 18 articles, what is the profit %?

Let cost price of 1 article be Re 1.

CP of 18 articles = 18

SP of 12 articles = 18

SP of 1 article = 18/12 = 1.5

Profit on 1 article = 1.5 - 1 = 0.5

Profit % = 0.5/1 × 100

= 50%

Example 7: By selling a radio for Rs. 1536, Suresh lost 20%. What percent shall he gain or lose by selling it for Rs. 2000?

SP = 1536, Loss % = 20%

CP = 100/(100 - 20) × 1536

= 100/80 × 1536 = 1920

New SP = 2000

Profit = 2000 - 1920 = 80

Profit % = 80/1920 × 100

= 4.16%

Example 8: Mohit sells a bicycle to Rohit at a gain of 10% and Rohit again sells it to Jyoti at a profit of 5% If Jyoti pays Rs. 462 to Rohit, what is the cost price of the bicycle for Mohit?

Here, there are two stages with 10% profit and then 5% profit.

Net Profit % = 10 + 5 + (10×5)/100 = 15.5

SP = 462

CP = 100/(100 + 15.5) × 462

= 100/115.4 × 462

= Rs. 400

Example 9: Rajesh sold two horses for Rs. 990 each; gaining 10% on the one and losing 10% on the other. Find his total gain or loss percent?

SP = 990

CP1 = 100/110 × 990 = 900

CP2 = 100/90 × 990 = 1100

Total CP = 2000

Total SP = 990 + 990 = 1980

Gain = 2000 - 1980 = 20

Gain % = 20/2000 × 100 = 1%

Example 10: A shopkeeper sold sarees at Rs. 266 each after giving 5% discount on labelled price. Had he not given the discount, he would have earned a profit of 12% on the cost price. What was the cost price of each saree?

Labelled Price or MP = SP + Discount

Discount % = Discount/MP × 100

5 = (MP - SP)/MP × 100

5 × MP = (MP - SP) × 100

MP = 100/95 × 266 = 280

Without discount, SP = 280

Profit = 12%

CP = 100/112 × 280

= Rs. 250