Question

A watch is sold by a salesman at a profit of $15%$. If the selling price of the watch had been rs. $48$ more , the profit percent would have been $18%$. At what price had the salesman bought the watch?

Answer 1

Hint:
For the above question, first suppose the cost price of the watch then find the selling price with the help of profit% and at last according to the question put all values and calculate it.

Complete step by step solution:
To calculate cost price of the watch,
Let us suppose the cost price (c.p.) is x rs.
Then
 selling price (s.p.) = profit + c.p. …………………..(i)
Now, we have to calculate profit to find the value of s.p. ,
 profit = $15\,%$of cost price
profit=$15\,%$ of $x$=$\dfrac{15}{100}x$
 Now we have value of profit and c.p. and on putting on equation (i), we get
s.p.= $\dfrac{15}{100}x$+$x$=$1.15x$
 Now according to the question, if the selling price is $rs.48$ then, profit % would be $18%$, so that
$18%\,\,of\,c.p.-15%\,\,of\,c.p.$=$48$
$\dfrac{18}{100}c.p.-\dfrac{15}{100}c.p.=48$
Now ,on calculating the above equation, we get
$\dfrac{3}{100}c.p.=48$
Then on transferring numbers one side , we get
$c.p.=\dfrac{48\times 100}{3}$
 We know that $48$ is divisible by $3$ we get
$c.p.=16\times 100=1600$

Therefore the required cost price of the watch is rs. $1600$.

Addition information:
Selling price- It is the price at which a good is sold by a shopkeeper to a customer.
Cost price-It is the price at which the goods bought by a customer.
Marked price- Marked price is the price that has been marked on the goods.

Note:
Sometimes in such problems marked price is given instead of selling price, a very little difference between them and students make mistakes in calculation. So that we should take care of all these mistakes.