Question

Find the single discount which is equivalent to successive discount of 20%, 15% and 10%.

Answer 1

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 = 15%
`"S.P."_2/"S.P"_1 = 1 - "discount"/(100)`

⇒ `"S.P."_2/(80) = 1 - (15)/(100)`

⇒ `"S.P."_2 = (85)/(100)` x Rs.80
= Rs.68

Third discount = 10%
`"S.P."_3/"S.P"_2 = 1 - "discount"/(100)`

⇒ `"S.P."_3/(68) = 1 - (10)/(100)`

⇒ `"S.P."_3 = (90)/(100)` x Rs.68
= Rs.61.2
∴ Net discount
= M.P. - S.P.₃
= Rs.(100 - 61.2)
= Rs.38.8
∴ Discount% = 38.8%.