Problems on Cost Price, Selling Price and Rates of Profit and Loss

In the previous topic of this chapter we have discussed about cost price, selling price, profit, loss, profit percent and loss percent. Let us revise them once in short. 

Cost price: cost price is the price at which a commodity is purchased by a shopkeeper from dealer or merchant.

Selling price: selling price is the price at which a commodity is sold by shopkeeper to the customers.

Profit: when a shopkeeper sells a commodity to a customer at a price more than the cost price, then he gets a profit.

Profit = selling price – cost price

           = S.P. – C.P.

Profit percent = \(\frac{S.P. - C.P.}{C.P.}\) x 100 %

Loss: When a shopkeeper sells a commodity to a customer at a price lower than the cost price, then he suffers a loss.

Loss = Cost Price – Selling Price

       = C.P. – S.P. 

Loss percent = \(\frac{C.P. - S.P.}{C.P.}\) x 100 %

Now let us solve some problems based upon these concepts.

1. A shopkeeper buys t-shirts from a dealer at rate of Rs 700 per t-shirt. He sells them at a rate of Rs 850 per t-shirt. He buys 10 t-shirts of same type and at same rate. Find the overall profit/loss. Also profit percent/ loss percent.

Solution:

cost price rate = Rs 700per t-shirt

Total cost price = Rs 700 x 10

                       = Rs 7000

Selling price rate = Rs 850 per t-shirt

Total selling price = Rs 8500

Since, total cost price is less than total selling price. So, the shopkeeper will have profit.

Profit = total selling price - total cost price

        = Rs 8500 - Rs 7000

        = Rs 1500

Profit percent = \(\frac{1500}{7000}\) x 100 %

                    = 21.42%

2. A shopkeeper sells a refrigerator for Rs12,500 with a loss of Rs1500. Find the price at which he had bought it from dealer. Also calculate the loss percent.

Solution:

Selling price of the refrigerator = Rs 12,500

Loss suffered by the shopkeeper = Rs 1,500

Cost price = ?

We know that, Selling price = Cost Price – Loss

So, Cost Price = Selling Price + Loss

Cost Price = Rs 12,500 + Rs1,500

               = Rs 14,000

Loss percent = \(\frac{Loss}{C.P.}\) x 100 %

                   =  \(\frac{1500}{14000}\) x 100%

                   = 10.715

3. A shopkeeper sells a refrigerator at cost price of Rs 15000 with a profit of 20%. Find the price at which customer has purchased it. Also find profit gained by the shopkeeper.

Solution:

Cost price = Rs 15000

Profit percent = 20%

Profit = cost price x profit percent

Profit = \(\frac{15000}{20} \times \frac{1}{100}\)

Profit = Rs 3,000

Selling price = cost price + profit

                   = Rs 15000 + Rs 3,000

                    = Rs 18,000

So, the amount payed by customer to the shopkeeper = Rs 18,000.

4. A shopkeeper sells a television set at Rs 25,000 to a customer making a profit of Rs 2,000 at the set. Find the price at which he must have bought it from the dealer. Also find the profit percent.

Solution:

Selling price of television set = Rs 25,000

Profit = Rs 2,000

We know that S.P. = C.P. + Profit

So, C.P. = S.P. – Profit

C.P. = Rs 25,000 – Rs 2,000

C.P. = Rs 23,000

Profit percent = \(\frac{S.P. - C.P.}{C.P.}\) x 100 %

                    = \(\frac{Profit}{C.P.}\) x 100 %

                    = \(\frac{2000}{23000}\) x 100 %

                    = 8.69%

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