Sum

The true discount on a sum is `3/8` of the sum due at 12% p.a. Find the period of the bill.

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#### Solution

Given, T.D. =`3/8 xx`S.D.

∴ T.D. = `3/8 xx ("P.W." + "T.D.")`

∴ `8/3` T.D. = P.W. + T.D.

∴ P.W. = `8/3` T.D. - T.D.

∴ P.W. = `5/3` T.D.

Also, T.D. = `("P.W." xx "n" xx "r")/100`

∴ T.D. =`(5/3 "T.D." xx"n" xx 12)/100`

∴ T.D. = `(5 "T.D." xx "n" xx 12)/(3 xx 100)`

∴ n = `("T.D." xx 3 xx 100)/(5 "T.D." xx 12)`

∴ n = 5 years

∴ Period of the bill is 5 years.

Concept: Discount

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