**Cost price:- **The price at which an article is purchased by a dealer is called its

cost price. (C.P)

**Selling price:- **The price at which an article is sold by a dealer is called its selling price (S.P)

**Profit:-** If the selling price of an article is more than its cost price, then the dealer makes a profit and ** profit = selling price – cost price Loss:- **If the selling price of an article is less than its cost price, then the dealer suffers a loss and

**loss = cost price – selling price**

## Formulae for Cost Price, Selling Price and Profit

In solving problems on profit and loss, remember the following :**Profit = S.P. – C.P. Loss = C.P. – S.P. Profit percentage = (profit/cost price × 100)% Loss percentage = (loss/cost price × 100)% **If there is a profit of p%, then

**S.P. = C.P. + profit = C.P. + p % of C.P.**

= C.P. + p/100 of C.P. = (1 + p/100) of C.P.

Thus,

= C.P. + p/100 of C.P. = (1 + p/100) of C.P.

**S.P. = (1 + p/100) of C.P.**

If there is a loss l %, then

**S.P = C.P. – loss**

= C.P. – l % of C.P.

= C.P. – l/100 of C.P.

= (1- l/100) of C.P.

Thus,

= C.P. – l % of C.P.

= C.P. – l/100 of C.P.

= (1- l/100) of C.P.

**S.P. = (1 – 1/100) of C.P.**

If C.P. and S.P. are given for different number of articles, first find C.P. and S.P. of equal number of articles and then calculate profit or loss percentage.

If an article is purchased for some amount and there are some additional expenses on transportation, labour, commission etc., these are to be included in the cost price. Such expenses are called overheads.

## Illustrative Examples for Cost Price, Selling Price and Profit

**For example:- **If an article is purchased for Rs 570 and Rs 30 are spent on its transportation, then the total cost of article = Rs 570 + Rs 30 = Rs 600. If the dealer sells it for Rs 645, then his profit = Rs 645 – Rs 600 = Rs 45

... Profit percentage = (45/600 × 100)% = 15/2% = 7.5%

Thus, overheads (if any) are always added to the original cost to get the total cost, and the profit or loss percentage is calculated on the total cost price.

**Example1.**John bought a watch for Rs 540 and sold it for Rs 585. Find his profit and profit percentage.

**Solution.**C.P. of the watch = Rs 540, S.P. of the watch = Rs 585

Profit = S.P. – C.P. = Rs 585 – Rs 540 = Rs 45

Profit percentage = (profit/C.P. × 100)% = (45/540 × 100)%

= 100/12% = 25/3% = 8,1/3%

**Example2.**By selling a bike for Rs 22464, Ansari incurs a loss of Rs 1536. Find his loss percentage.

**Solution.**S.P. of the bike = Rs 22464, loss = Rs 1536

... C.P. of the bike = S.P. + loss = Rs 22464 + Rs 1536

= Rs 24000

Loss percentage = (loss/C.P. × 100)% = (1536/24000 × 100)%

= 1536/24% = 34/10% = 6.4%

**Example3.**Bijoy bought bananas at the rate of 5 for Rs 4 and sold them at the rate of 4 for Rs 5. Calculate.

(i) His gain percent.

(ii) The number of bananas he should sell to earn to profit of Rs 90.

**Solution.**

(i) C.P. of 5 bananas = Rs 4

C.P. of 1 banana = Rs 4/5 = Rs 0.80

S.P. of 4 bananas = Rs 5

S.P. of 1 banana = Rs 5/4 = Rs 1.25

... Gain on the sale of one banana = S.P. – C.P.

= Rs 1.25 – Rs 0.80 = Rs 0.45

... Gain percentage = (profit/C.P. × 100)% = (0.45/0.80 × 100)%

= (45/80 × 100)% = 225/4% = 56.25%

(ii) Number of bananas to be sold = total profit/profit on one banana

= Rs 90/Rs 0.45 = 90/0.45 = 200

**Example4.**A fruit-vendor buys certain number of oranges. If the selling price of 6 oranges is equal to the cost price of 5 oranges, find his profit or loss percentage.

**Solution.**Let the cost price of one orange be Rs x, then

C.P. of 5 oranges = Rs 5x

It is given that S.P. of 6 oranges = C.P. of 5 oranges

... S.P. of 6 oranges = Rs 5x

... S.P. of one oranges = Rs 5x/6

As the cost price of one orange is Rs x and the selling price of one orange is Rs 5x/6, the fruit-vendor suffers a loss.

His loss on selling one orange = Rs x – Rs 5x/6

= Rs 6x – 5x/6 = Rs x/6

... Loss percentage = (loss/C.P. × 100)% = (x/6/x × 100)%

= 100/6% = 50/3% = 16 2/3%

## Problem to Solve on Cost Price, Selling Price and Profit

1. A shopkeeper purchased one dozen pens for Rs 108 and sold these at Rs 12.50 each. Find :

(*i*) The cost of one pen.

(*ii*) Profit or loss on selling one pen.

(*iii*) His total profit or loss on selling all pens.

2. A fruit seller bought 600 bananas at 6 for Rs 5 and sold at 5 for Rs 6. Find :

(*i*) The cost price of all bananas

(*ii*) The selling price of all bananas.

(*iii*) His profit and profit percentage on the whole deal.

3. A shopkeeper purchased 10 dozen pencils at Rs 20 a dozen. He sold all the pencils at two rupees piece. Find his total profit or loss. Also calculate it as a percentage.

4. Mr. Mehta purchased a second hand car for Rs 80000 and spent Rs 15000 on repairs. After some time, he sold the car for Rs 90000. Find the profit or loss. Also calculate it as percentage.

5. A dealer purchased 100 quintals of wheat at Rs 550 a quintal. He spent Rs 10000 on transportation and storage. He then sold the wheat at Rs 6.50 per kg. Find his profit or loss.

## Things to Remember

• The price at which an article is bought by a dealer is called its cost price (C.P.)

• The price at which an article is sold by a dealer is called its selling price (S.P.)

• If the selling price is more than the cost price, then the dealer makes a profit.

and profit = selling price - cost price

• If the selling price is less than the cost price, then the dealer suffers a loss

and loss = cost price - selling price

• Profit or loss percentage is calculated on the cost price.

Profit percentage = (profit/cost price × 100)%

Loss percentage = (loss/cost price × 100)%

• If there are any overhead expenses, then these are to be added in the cost price.