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प्रश्न
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.
उत्तर
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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Solution: Banker’s Discount
B.D.= F.V. − C.V. = 8,000 −7,680 = ₹ 320
Date of drawing = 5th January 2019
Period = 8 months
Nominal due date = `square`
Legal due date = `square`
B.D. = Interest on F.V. for n at 10% p.a.
∴ B.D. = `("F.V." xx "n"/365 xx "r")/100`
∴ 320 = `(8000 xx "n"/365 xx 10)/100`
∴ n = `square` days
| April | May | June | July | Aug | Sep | Total |
| 15 | 31 | 30 | 31 | 31 | `square` | `square` |
∴ Date of discounting is `square`
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