Question

Find the single discount which is equivalent to successive discounts of 10%, 8% and 5%.

Answer 1

Let the marked price be Rs.100
First discount = 10%
`"S.P."_1/"M.P." = 1 - "discount"/(100)`

⇒ `"S.P."_1/(100) = 1 - (10)/(100)`

⇒ `"S.P."_1 = (90)/(100)` x Rs.100
= Rs.90

Second discount = 8%
`"S.P."_2/"S.P"_1 = 1 - "discount"/(100)`

⇒ `"S.P."_2/(90) = 1 - (8)/(100)`

⇒ `"S.P."_2 = (92)/(100)` x Rs.90
= Rs.82.8

Third discount = 5%
`"S.P."_3/"S.P"_2 = 1 - "discount"/(100)`

⇒ `"S.P."_3/(82.8) = 1 - (5)/(100)`

⇒ `"S.P."_3 = (95)/(100)` x Rs.82.8
= Rs.78.66
∴ Net discount
= M.P. - S.P.₃
= Rs. (100 - 78.66)
= Rs.21.34
∴ Discount% = 21.34%.