Question

The difference between true discount and banker's discount on a bill due 6 months hence at 4% is ₹ 160. Calculate true discount, banker's discount and amount of bill.

Answer 1

Let T.D. = ₹ x, n = `6/12 = 1/2` year

B.G. = B.D. – T.D.

= Interest on T.D. for 6 months at 4% p.a.

∴ 160 = `x xx 1/2 xx 4/100 = x/50`

x = 8,000

∴ True discount ₹ = 8,000

B.D. = B.G. + T.D.

= 160 + 8,000

= 8,160

∴ Banker's discount = ₹ 8,160

B.D. = Interest on FV for 6 months at 4 % p.a.

Let the face value (F.V.) be y.

∴ B.D. = `y xx 1/2 xx 4/100`

8,160 = `y/50`

y = ₹ 4,08,000

∴ Amount of bill is ₹ 4,08,000.