The shopkeepers mark up the price of LED, 60% above its cost price and give three successive discounts of 12.5%, d% and 25%. If shopkeeper made a loss of 16% on LED, then find the second discount allowed by the shopkeeper.

Explanation

Let the cost price of the LED be 100x. Marked price = 160x. Selling price = 160x × (100 – 12.5)/100 × (100 – d)/100 × (100 – 25)/100 = 105x × (100 – d)/100. Loss% = (cost price – selling price)/cost price ⇒ 16/100 = [100x – 105x × (100 – d)/100]/100x ⇒ 105 × (100 – d)/100 = 84 ⇒ d = 20%. ∴ The required discount% is 20%.