Successive discounts of 20%, 10% and 15% are equivalent to a single discount of?

A. 42.2%

B. 38.8%

C. 43.5%

D. 44.5%

Detailed Solution: 

The correct answer is 38.8%

Given:

The successive discounts are 20%, 10%, and 15%.

Formula:

Successive discount = X + Y - (XY)/100

Where,

X = First discount

Y = Second discount

Calculation:

Successive discount = X + Y - (XY)/100

⇒ 20 + 10 - 200/100

⇒ 28%

Now, again

Successive discount = X + Y - (XY)/100

X = 28%, Y = 15%

⇒ 28 + 15 - (28 × 15)/100

⇒ 28 + 15 - 420/100

⇒ 43 - 4.2% = 38.8%

∴ The single equivalent discount is 38.8%.

Let the amount be 100.

Successive discount on 100 = (100 - 80% of 90% of 85% of 100)

⇒ 100 - 61.2 = 38.8%