A shirt with a list price of Tk. 150 is sold for Tk. 105 after two successive discounts. If the second discount is 12.5%, what was the rate of the first discount?

Question: A shirt with a list price of Tk. 150 is sold for Tk. 105 after two successive discounts. If the second discount is 12.5%, what was the rate of the first discount?

Solution:
Let the first discount be x%.

∴ After the first discount,
∴ the price = (100 − x)% of 150
= (100 − x)/100 × 150

After the second discount of 12.5%,
the selling price = 87.5% of the first discounted price
= 87.5/100 × (100 − x)/100 × 150

Given selling price = 105,
ATQ,
87.5/100 × (100 − x)/100 × 150 = 105
⇒ 100 − x = (105 × 100 × 100) / (87.5 × 150)
⇒ 100 − x = 80

∴ x = 100 − 80
= 20

∴ The first discount is 20%.