Three successive discounts of 10 %,12 %,and 1 | vedclass

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(B) To find the equivalent single discount for three successive discounts of $x \%$,$y \%$,and $z \%$,we use the formula:$	ext{Equivalent Discount} =

Vedclass · Accepted Answer

$32.68$

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(B) To find the equivalent single discount for three successive discounts of $x \%$,$y \%$,and $z \%$,we use the formula:$	ext{Equivalent Discount} = \left[ x + y + z - \frac{xy + yz + zx}{100} + \frac{xyz}{100^2} ight] \%$Given $x = 10$,$y = 12$,and $z = 15$:$1. 	ext{ Sum of discounts} = 10 + 12 + 15 = 37$$2. 	ext{ Sum of products taken two at a time} = (10 	imes 12) + (12 	imes 15) + (15 	imes 10) = 120 + 180 + 150 = 450$$3. 	ext{ Product of all three} = 10 	imes 12 	imes 15 = 1800$Substituting these values into the formula:$	ext{Equivalent Discount} = \left[ 37 - \frac{450}{100} + \frac{1800}{10000} ight] \%$$= [37 - 4.5 + 0.18] \%$$= 32.68 \%$

Three successive discounts of $10 \%$,$12 \%$,and $15 \%$ are equivalent to a single discount of what percentage (in $\%$)?

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