Question

by reducing the selling price of an article by rupees 50 a gain of 5% turn into a loss of 5% find the original selling price of the article ​

Answer 1

Let Rs. 'x' be the cost price and Rs. 'y' be the original selling price of the article.

We know that,

Gain % = (Gain*100/cost price)

∴ 5 % = (y - x)*100/x

⇒ x = 20(y - x)

⇒ x = 20y - 20x

⇒ x + 20x = 20y

⇒ 21x = 20y

⇒ y = 21x/20

When the selling price of the article is reduced by Rs. 50 then the new selling price of the article = Rs.(21x/20 - 50)

We know that,

Loss % = (Loss*100)/Cost price 

5 = [x - {21x/20 - 50}/x)] × 100

⇒ x = {x - 21x/20 + 50} × 20

⇒ x = [{20x - 21x +1000}/20] ×20

⇒ x = - x + 1000

⇒ x + x = 1000

⇒ 2x = 1000

⇒ x = 500

So, the cost price of the article is Rs. 500.

The original selling price 'y' = 21x/20

= (21*500)/20

y = 525

The original selling price is Rs. 525

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