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

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Updated on: September 25th, 2023 (A) 38.8%

(B) 43.5%

(C) 42.2%

(D) 44.5%

Successive discounts of 20%, 10%, and 15% are equivalent to a single discount of 38.8%. To understand this, you need to do clear calculations for this.

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%

Summary:

## Successive discounts of 20%, 10% and 15% are equivalent to a single discount of (A) 38.8% (B) 43.5% (C) 42.2% (D) 44.5%

A single discount of 38.8% is similar to three successive discounts of 20%, 10%, and 15%. To find the successive discount, use this formula of Successive discount = X + Y – (XY)/100. where X is first discount and Y is second discount.

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