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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.
Solution
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.
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