Question

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

Answer 1

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

∴ T.D. = `3/8` × (P.W. + T.D.)

∴ `8/3` T.D. = P.W. + T.D.

∴ P.W. = `3/8` T.D. − T.D.    ...[Multiply both sides by 8]

8T.D. = 3(P.W. + T.D.)

8T.D. = 3P.W. + 3T.D.

Now bring like terms together:

8T.D. − 3T.D. = 3P.W.

5T.D. = 3P.W.

∴ 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

∴ The bill has a 5-year term.