Question

by selling a wall clock at a loss of 20% A shopkeeper includes a loss of rupees 80 find the cost price and selling price

Answer 1

Given :

Loss percent of a wall clock : 20%

Loss rupees of a wall clock : ₹80

To find :

The cost price and the selling price of the wall clock.

Solution :

First, we'll find the value of the cost price.

Let the cost price of the wall clock be y.

Cost price of the wall clock :

$\sf \dashrightarrow y - (20\% \: of \: y) = 80$

$\sf \dashrightarrow y - \bigg( \dfrac{20}{100} \: of \: y \bigg) = 80$

$\sf \dashrightarrow y - \bigg( \dfrac{20}{100} \times y \bigg) = 80$

$\sf \dashrightarrow y - \bigg( \dfrac{1}{5} \times y \bigg) = 80$

$\sf \dashrightarrow y - \dfrac{y}{5} = 80$

$\sf \dashrightarrow \dfrac{5y - y}{5} = 80$

$\sf \dashrightarrow \dfrac{4y}{5} = 80$

$\sf \dashrightarrow 4y = 80 \times 5$

$\sf \dashrightarrow 4y = 400$

$\sf \dashrightarrow y = \dfrac{400}{4}$

$\sf \dashrightarrow y = 100$

Now, we can find the selling price of the clock.

Selling price of wall clock :

$\sf \dashrightarrow \dfrac{(100 - Loss\%)}{100} \times CP$

$\sf \dashrightarrow \dfrac{(100 - 20)}{100} \times 100$

$\sf \dashrightarrow \dfrac{80}{100} \times 100$

$\sf \dashrightarrow \dfrac{4}{5} \times 100$

$\sf \dashrightarrow \dfrac{4 \times 100}{5} = \dfrac{400}{5}$

$\sf \dashrightarrow \cancel \dfrac{400}{5} = 80$

Hence, the cost price and the selling price of the wall clock is ₹100 and ₹80 respectively.