Question

A shopkeeper sold a watch at 5% profit.If he had sold it for 72 rupees more,he would have gained 13% profit.How much did he invest in the watch?​

Answer 1

₹900

Step-by-step explanation:

Let the invested money for the watch be x. (cost price)

Firstly, the shopkeeper sold the watch at 5% profit.

$\bullet\quad\boxed{\rm Selling \ price =\Bigg ( \dfrac{100+Profit\%}{100} \Bigg )Cost \ Price }$

Cost Price = x, Profit % = 5

Hence,

$\dashrightarrow\rm Selling \ price =\Bigg ( \dfrac{100+5}{100} \Bigg )x$

$\dashrightarrow\bf \dfrac{105}{100}x$

Similarly, for the second condition ,

Cost Price = x, Profit % = 13

$\dashrightarrow\rm \Bigg ( \dfrac{100+13}{100} \Bigg )x$

$\dashrightarrow\bf \dfrac{113}{100}x$

If he had sold it for 72 rupees more,he would have gained 13% profit.

Hence, difference between both the selling price will be 72.

$\dashrightarrow\rm \dfrac{113}{100}x-\dfrac{105}{100}x =72$

$\dashrightarrow\rm \dfrac{113-105}{100}x =72$

$\dashrightarrow\rm \dfrac{8}{100}x =72$

$\dashrightarrow\rm \dfrac{2}{25}x =72$

$\dashrightarrow\rm x =\dfrac{25\times 72}{2} = \bf 900$

Hence, the money he invested is ₹900