Question

In a stock clearance sale, a shoe company reduces the prices by 20%. If the discounted price of a pair of shoes is Rs. 560, find its original price.

Answer 1

Hint: Here, we will assume the original price to be some unknown variable let say x. Then we will use the formula of discounted price which can be found using the formula: Discounted price=$CP-discount\%\text{ }of\text{ }CP$ where CP is the original price. Hence, from this we will the value of CP, which is the answer.

Complete step-by-step answer:
Here, we are given that prices of shoes are reduced to 20%. Also, after discount the price of shoes is Rs. 560. So, we have to find the original price which is considered as the CP.
 We will assume the CP of shoes to be let’s say Rs. X.
 So, we will use the formula of discount which is given as Discounted price=$CP-discount\%\text{ }of\text{ }CP$
So, on substituting the values we have,
$\Rightarrow 560=x-20\%x$
$\Rightarrow 560=x-\dfrac{20}{100}x$
On simplifying, we get
$\Rightarrow 560=x-\dfrac{2}{10}x$
Taking x common from RHS, we get
$\Rightarrow 560=x\left( 1-\dfrac{2}{10} \right)$
Taking LCM on RHS and then multiplying with 10 on both sides, we get
$\Rightarrow 5600=x\left( 10-2 \right)$
$\Rightarrow 5600=8x$
$\Rightarrow \dfrac{5600}{8}=x$
$\Rightarrow x=700$ Rs.
Thus, we get original price i.e. cost price CP as Rs. 700.

Note: Students sometimes make mistake directly by using the concept as how much of 20% will give the answer are discount price i.e. Rs. 560. So, they simply use the formula as
$20\%x=560$
On solving we get,
$\Rightarrow \dfrac{20}{100}x=560$
$\Rightarrow x=560\times 5=Rs.2800$
This answer is wrong. So, you must verify by calculation that CP is Rs. 2800 and after 20% discount value will be 560. So, this Rs, 560 should be subtracted from CP to get the final discounted price. Here, on doing this we get a discounted price as $Rs.2800-Rs.560=Rs.2240$ . Thus, this answer does not match with our question discounted price. So, don’t make this mistake.