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Question
Find the single discount which is equivalent to successive discounts of 20%, 10% and 5%. Hence, find the selling price of an article marked at Rs. 2500.
Solution
Let the M.P. be of the article be Rs. x and a single discount be d % be equivalent to three given successive discounts of 20%, 10% and 5%.
Equating the two selling prices of the article we get
`(1 - "d"/100)` of Rs. x
= `(1 - 20/100)(1 - 10/100)(1 - 5/100)` of Rs. x
⇒ `(1 - "d"/100) xx x = (80)/(100) xx (90)/(100) xx (95)/(100) xx x`
⇒ `1 - "d"/(100) = (80)/(100) xx (90)/(100) xx (95)/(100)`
⇒ `1 - "d"/(100) = (684000)/(1000000)`
⇒ `1 - (684000)/(1000000) = "d"/(100)`
⇒ `(316000)/(1000000) = "d"/(100)`
⇒ d = `(316000 xx 100)/(1000000)`
⇒ d = 3.16%
M.P. of the article = Rs.2500
S.P. = `(1 - 31.6/100) xx 2500`
⇒ S.P. = `(68.4)/(100) xx 2500`
⇒ S.P. = Rs.1710
Hence, the equivalent discount is Rs.31.6% and the S.P. is Rs.1710.
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