A shopkeeper offers two successive discounts of 15% and 20% on an article and is still able to earn a 70% profit. If he offers a single discount of 30%, what will his profit percentage be?

Let's assume the MRP of the article is 100y.

A shopkeeper offers two successive discounts of 15% and 20% on an article.

Selling price of the article = 100y of (100-15)% of (100-20)%

= 100y of 85% of 80%

= $$100y\times\frac{85}{100}\times\frac{80}{100}$$

= 68y

He is still able to earn a 70% profit.

Cost price of the article = $$\frac{68y}{\left(100+70\right)}\times\ 100$$

= $$\frac{68y}{170}\times\ 100$$

= 40y

If he offers a single discount of 30%, then selling price = 100y of (100-30)%

= 100y of 70%

= 70y

New profit percentage = $$\frac{\left(70y-40y\right)}{40y}\times100$$

= $$\frac{30y}{40y}\times100$$

= 75%