Question

A retailer buys a radio for Rs. 225. His overhead expenses are Rs. 15. If he sells the radio for Rs. 300, then determine his profit(in percent).

Answer 1

Hint: Use the fact that gain is equal to selling price subtracted from cost price, i.e. gain= S.P -C.P. Gain % is the amount of gain per 100 units of C.P. Using a unitary method find the gain % in this whole transaction. Alternatively, use $gain%=\dfrac{gain}{C.P}\times 100$ to get the gain% earned by the retailer in this transaction.

Complete step-by-step answer:
We have the cost at which the radio was purchased by the retailer = Rs. 225
The overhead expenses that were taken up by the retailer = Rs. 15
The amount for which the radio was sold by the retailer = Rs. 300
Hence the gain earned by the retailer = Rs 300-Rs (225+15) = Rs. (300-240) =Rs. 60
(Because the overhead charges are also taken up by the retailer, so, they also go into the cost price)
Hence the gain earned by the retailer is equal to Rs.60
Gain % is defined as the amount of gain earned per 100 units of cost price.
We have, the gain on Rs 60 of C.P = Rs. 240
Hence, we have
The gain on Re. 1 of C.P $=\dfrac{60}{240}=\dfrac{1}{4}$
Hence gain per Rs. 100 of C.P $=\dfrac{1}{4}\times 100=25%$
Hence the gain % of the retailer = 25%

Note: We can directly calculate gain using the formula
$gain%$=$\dfrac{gain}{C.P}\times 100$
Substituting the values of gain and C.P, we get
$gain%$=$\dfrac{60}{240}\times 100=25%$