Question

A shopkeeper sold an article at 20 % discount and made a loss of Rs 90. If he had
sold it at 5 % discount, he would have gained Rs 90. Find the cost price and the
marked price of the article.
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Answer 1

Answer:

The cost price of the article is Rs 1050

The marked price of the article Rs 1200

Step-by-step explanation:

The given discount on the article = 20%

The amount loss  = Rs 90

With a discount of 5% the amount gained = Rs 90

Let the cost price of the article = X

Let the marked price of the article = Y

Therefore, we have;

(1 - 0.2) × Y = X - Rs 90

(1 - 0.5) × Y = X + Rs 90

Which gives;

0.8·Y = X - Rs 90 .......................(1)

0.95·Y = X + Rs 90.....................(2)

Subtracting equation (1) from equation (2), we have;

0.95·Y-0.8·Y = X + Rs 90 - (X - Rs 90) = X - X + Rs 90 + Rs 90 = Rs 180

0.15·Y = Rs 180

Y = Rs 180/0.15 = Rs 1200

Therefor, the marked price of the article = Rs 1200

From;

0.8·Y = X - Rs 90, we have;

0.8×Rs 1200 = X - Rs 90

X = 0.8× 1200 + 90 = Rs 1050

Therefore, the cost price of the article = Rs 1050.