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प्रश्न
A bill of ₹ 51,000 was drawn on 18th February 2010 for 9 months. It was encashed on 28th June 2010 at 5% p.a. Calculate the banker’s gain and true discount.
उत्तर
It is given that,
Face value (F.V.) = ₹ 51,000 which is (S.D.)
Date of drawing = 18th February 2010
Date of discounting = 28th June 2010
Period of bill = 9 months
Nominal due date = 18th November 2010
Legal due date = 21st November 2010
Number of days from date of discounting bill to legal due date
| June | July | Aug | Sep | Oct | Nov | Total |
| 2 | 31 | 31 | 30 | 31 | 21 | 146 days |
Rate = 5% p.a.
We know that,
T.D. = `("P.W." xx "n" xx "r")/100`
`= ("P.W." xx 146/365 xx 5)/100`
∴ T.D. = 0.02 P.W. ...(i)
Since, S.D. = P.W. + T.D.
∴ S.D. = P.W. + 0.02 P.W. …[From (i)]
∴ 51,000 = 1.02 P.W.
∴ P.W. = `(51,000)/1.02`
∴ P.W. = 50,000
Since T.D. = 0.02 × P.W.
= 0.02 × 50000
= ₹ 1000
∴ True discount is ₹ 1,000
Banker’s gain = `("T.D." xx "n" xx "r")/100`
`= (1000 xx 146/365 xx 5)/100`
= ₹ 20
∴ True discount is ₹ 1,000 and Banker’s gain is ₹ 20.
Notes
The answer in the textbook is incorrect.
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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`
