Question

Find the true discount, banker’s discount and banker’s gain on a bill of ₹ 4,240 due 6 months hence at 9% p.a.

Answer 1

Given, S.D. = ₹ 4,240,

n = `6/12 = 1/2` years, r = 9% p.a.

Since, B.D. = `("S.D." xx "n" xx "r")/100`

∴ B.D. = `(4,240 xx 1/2 xx 9)/100`

`= (4,240 xx 9)/(100 xx2)`

∴ B.D. = ₹ 190.80

Let true discount be ₹ x

Now, B.D. = T.D. + Interest on T.D. for `1/2` year at 9% p.a.

∴ 190.80 = `x + (x xx 1/2 xx 9/100)`

∴ `190.80 = x + (9x)/200`

∴ `190.80 = (209 x)/200`

∴ x = `(190.80 xx 200)/209`

∴ x = ₹ 182.58

∴ T.D. = ₹ 182.58 ≈ ₹ 182.60

Also, B.G. = B.D. – T.D. = 190.8 – 182.58

∴ B.G. = ₹ 8.22 ≈ ₹ 8.20

∴ True discount, banker’s discount and banker’s gain are ₹ 182.60, ₹ 190.80 and ₹ 8.20 respectively.