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.

Answer 1

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.