Question

If one shirt price is \[Rs.220\]at \[12\% \]discount. What is the original price of the shirt before the discount?

Answer 1

Hint: In this question, we are given that the shirt cost \[Rs.220\]after a discount of \[12\% \]and we have to find the original price of the shirt. When we are given \[12\% \]discount, that means the discount is on the original price and when we subtract this amount of discount from the original price, we will get the discounted price, which is given to be \[Rs.220\].So, we now have to frame the equation by letting the original price to be \[Rs.x\]and then subtracting \[12\% \]of the original price \[i.e.12\% \]of \[x\]from the original price to get the discounted price which is given to be \[Rs.220\].
i.e. we will have \[Rs.x - 12\% \]of \[Rs.x = Rs.220\]
Then, after solving this equation, we will get the value of \[x\], which is the required original cost.

Complete step-by-step solution:
Let the original price be \[Rs.x\]
We are given that the discount is \[12\% \], which will be obviously on the original cost
So, the discount amount \[ = 12\% \]of \[Rs.x\] \[ = \dfrac{{12}}{{100}}\]of \[Rs.x\]
\[ = \dfrac{{12}}{{100}} \times Rs.x\]
\[ = \dfrac{3}{{25}} \times Rs.x\]
\[ = Rs.\dfrac{{3x}}{{25}}\]
So, now to find the discounted price, we need to subtract the discount amount from the original price.
Hence, The Discounted Price \[ = \]Original Price – Discount amount
\[ = Rs.x - Rs.\dfrac{{3x}}{{25}}\]
\[ = Rs.(x - \dfrac{{3x}}{{25}})\]
\[ = Rs.(\dfrac{{x \times 25 - 3x}}{{25}})\] (Taking LCM)
\[ = Rs.(\dfrac{{25x - 3x}}{{25}})\]
 \[ = Rs.(\dfrac{{22x}}{{25}})\]
Therefore, The Discounted Price \[ = Rs.\dfrac{{22x}}{{25}}\]
Also, we are given that The Discounted Price \[ = Rs.220\]
Equating the above two equations, we get
\[Rs.\dfrac{{22x}}{{25}} = Rs.220\]
\[\Rightarrow Rs.\dfrac{{22}}{{25}} \times x = Rs.220\]
 \[\Rightarrow x = \dfrac{{Rs.220}}{{Rs.\dfrac{{22}}{{25}}}}\] (Shifting the terms)
 \[\Rightarrow x = \dfrac{{Rs.220 \times 25}}{{Rs.22}}\]
\[\Rightarrow x = 10 \times 25 = 250\]
So, the original price of the shirt is \[Rs.250\].

Note: While reading the statement of the question, we need to understand very properly what the question says and what we are supposed to find out. In this question, we are given the price after discount so, we must know that that the discount is always on the original price and it needs to be subtracted from the original price then only, we can find out the price after discount. Also, while shifting the terms, we should be very careful with the signs that are to be changed while shifting.