A single discount equivalent to the successive discounts

A single discount equivalent to the successive discounts of 10 %, 20 % and 25 % is

First Method to solve this question.
Single of discount for successive discounts 10 % and 20 %

=		20 + 10 −	20 × 10		% = 28 %
			100

∴ Equivalent discount for discounts 28% and 25%

=		28 + 25 −	28 × 25		%
			100

= 53 – 7 = 46%
Second method :
Single equivalent discount

= 100 −

100 − D₁

100 − D₂

100 − D₃

× 100

100

= 100 −

100 − 10

100 − 20

100 − 25

× 100

100

= 100 −	90	×	80	×	75	× 100
	100		100		100

= 100 – 54 = 46%