A single discount equivalent to the series of discounts

A single discount equivalent to the series of discounts 20%, 10% and 5% is equal to :

Single equivalent discount for x% and y%.

=		x + y −	xy		%
			100

∴ Single equivalent discount for 20% and 10%

=		20 + 10 −	20 × 10		% = 28%
			100

Single equivalent discount for 28% and 5%

=		28 + 5 −	28 × 5		%
			100

=		33 −	140		%
			100

= (33 – 1.4)% = 31.6%
2nd Method to solve this question :
According to given question.
D₁ = 20%, D₂ = 10%, D₃ = 5%
Single equivalent discount

= 100 −

100 − D₁

100 − D₂

100 − D₃

× 100

100

= 100 −

100 − 20

100 − 10

100 − 5

× 100

100

= 100 −	80	×	90	×	95	× 100
	100		100		100

= 31.6%