Question

A shopkeeper gives two successive discounts on an article whose marked price is ₹ 180 and selling price is ₹ 108. Find the first discount percentage if the second discount is 25%

Answer 1

Marked price is given as ₹ 180

Let 1^st discount be d₁ % = ? ...(to find)

2^nd discount be d₂ % = 25%

Selling price is 108 ...(given)

Price after 1^st discount = `180(1 - ("d"_1)/100)` = P ...(1)

Price after 2^nd discount = `"P"_1 (1 - ("d"_2)/100)` = 108

Substituting for P₁ from (1), we get

`180(1 - ("d"_1)/100)(1 - ("d"_2)/100)` = 108

⇒ Since d₂ = 25, we get

`180(1 - ("d"_1)/100)(1 - 25/100)` = 108

∴ `(1 - ("d"_1)/100) = 108/180 xx 100/75 = 4/5`

`1 - ("d"_1)/100 = 4/5`

∴ `("d"_1)/100 = 1 - 4/5 = 1/5`

∴ d₁ = `1/5 xx 100` = 20%

1^st discount = 20%