Question

By selling a watch for Rs.720, Ravi loses 10%. At what price should he sell it, in order to gain 15%?

Answer 1

Hint: This problem deals with the profit and loss of a good. Here we are asked to find the selling price of a good when given the profit percentage. We have to find the cost price of the good first from the given loss percentage, in order to calculate the selling price for profit. If profit is $P$, loss is $L$, selling price and cost price are $SP$ and $CP$ respectively. The profit and loss percentage formulas are given by:
$ \Rightarrow P = \dfrac{{SP - CP}}{{CP}} \times 100$
$ \Rightarrow L = \dfrac{{CP - SP}}{{CP}} \times 100$

Complete step-by-step answer:
The profit percentage is calculated by the ratio of the difference of the selling price and the cost price and the cost price.
Whereas the loss percentage is calculated by the ratio of the difference of the cost price and the selling price and the cost price.
Given that Ravi has a loss percentage of 10% of selling his watch.
The selling price of the watch for the loss of percentage is Rs.720
Here $SP = 720$ and Loss, $L = 10\% $, substituting in the loss formula to get the cost price, $CP$.
$ \Rightarrow L = \dfrac{{CP - SP}}{{CP}} \times 100$
$ \Rightarrow \dfrac{{10}}{{100}} = \dfrac{{CP - 720}}{{CP}}$
Simplifying the above equation in order to get the value of the cost price.
$ \Rightarrow 0.1CP = CP - 720$
$ \Rightarrow 0.9CP = 720$
$\therefore CP = 800$
The cost price of the watch is Rs.800.
For the profit of 15%, $P = 15\% $ the selling price should be, as given below:
$ \Rightarrow P = \dfrac{{SP - CP}}{{CP}} \times 100$
$ \Rightarrow \dfrac{{15}}{{100}} = \dfrac{{SP - 800}}{{800}}$
On simplifying the above expression to get the value of the selling price.
$ \Rightarrow 0.15 = \dfrac{{SP - 800}}{{800}}$
$ \Rightarrow 120 = SP - 800$
$\therefore SP = 920$
Thus the selling price of the watch in order to gain a profit of 15% is Rs.920

Final Answer: The selling price is Rs.920 for Ravi to gain a profit of 15%.

Note:
Please note that while solving this problem of profit and loss, one thing we need to keep in mind is that the loss is nothing but the difference of cost price and the selling price, as in a loss selling price is less than the cost price, and hence it is called a loss.