If a company gives a discount of 20% on the marked price…

If a company gives a discount of 20% on the marked price of an article and gains 20% on that particular article, then at what percentage above the cost price did the company mark its goods?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 50%

Given:

Discount = 20%

Gain = 20%

Concept Used:

1. $S.P. = M.P. × {(100-D) \over 100}$ ....(i)

2. $C.P. = S.P.× {100 \over (100+ P)}$ .....(ii)

Where, S.P. = Selling Price

M.P. = Marked Price

C.P. = Cost Price

D = Discount

P = Gain/Profit

Explanation:

Let the marked price of the article be Rs. 100

$S.P. = 100 × {(100 - 20)\over 100}$ {using equation (i)}

⇒ S.P. = 80 .....(iii)

Now, $C.P. = 80 × {100 \over (100 + 20)}$ {using equation (ii) and (iii)}

⇒ C.P. = 80 × 100/120

⇒ C.P. = 200/3 ....(iv)

So, according to given question,

M.P. - C.P. = 100 - 200/3

M.P. - C.P. = 100/3

Now, required percentage = {(100/3) ÷ (200/3)} × 100

⇒ 1/2 × 100 = 50

Hence the required percentage is 50%.

SSC CHSL 2022 PYQ — Question 55