The single discount which is equivalent to successive discounts

The single discount which is equivalent to successive discounts of 20%, 15% and 10% is

Use the below formula to calculate the Equivalent single discount.

Equivalent single discount =		D₁ + D₂ −	D₁ × D₂		%
			100

Single equivalent discount for 20% and 15%

=		20 + 15 −	20 × 15		% = 32%
			100

Single equivalent discount for 32% and 10%

=		32 + 10 −	32 × 10		% = 38.8%
			100

Alternate method to solve this question :
Here, D₁ = 20%, D₂ = 15%,D₃ = 10%
Single equivalent discount

= 100 −

100 − D₁

100 − D₂

100 − D₃

× 100

100

= 100 −

100 − 20

100 − 15

100 − 10

× 100

100

Equivalent single discount = 100 −	80	×	85	×	90	× 100
	100		100		100

Hence Equivalent single discount = 100 – 61.20 = 38.80%