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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 marked price be Rs.100
First discount = 20%
`"S.P."_1/"M.P." = 1 - "discount"/(100)`
⇒ `"S.P."_1/(100) = 1 - (20)/(100)`
⇒ `"S.P."_1 = (80)/(100)` x Rs.100
= Rs.80
Second discount = 10%
`"S.P."_2/"S.P"_1 = 1 - "discount"/(100)`
⇒ `"S.P."_2/(80) = 1 - (10)/(100)`
⇒ `"S.P."_2 = (90)/(100)` x Rs.80
= Rs.72
Third discount = 5%
`"S.P."_3/"S.P"_2 = 1 - "discount"/(100)`
⇒ `"S.P."_3/(72) = 1 - (5)/(100)`
⇒ `"S.P."_3 = (95)/(100)` x Rs.72
= Rs.68.4
∴ Net discount
= M.P. - S.P.3
= Rs. (100 - 68.4)
= Rs.31.6
∴ Discount% = 31.6%
`"S.P."/"M.P." = 1 - "discount"/(100)`
⇒ `"S.P."/(2500) = 1 - (31.6)/(100)`
⇒ S.P. = `(68.4)/(100)` x Rs.2500
= Rs.1710.
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