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प्रश्न
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.
उत्तर
Given, S.D. = ₹ 4,240
n = `6/12 = 1/2` year, r = 9% p.a.
Since, B.D. = `("S.D." xx "n" xx "r")/100`
∴ B.D. = `(4,240 xx 1/2 xx 9)/100`
= `(4,20 xx 9)/(100 xx 2)`
∴ 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 = `(209x)/200`
∴ x = `(190.80 xx 200)/209`
∴ x = ₹ 182.58
∴ T.D. = ₹ 182.58
Also, B.G. = B.D. – T.D. = 190.8 – 182.58
∴ B.G. = ₹ 8.22
∴ True discount, banker’s discount and banker’s gain are ₹ 182.58, ₹ 190.80 and ₹ 8.22 respectively.
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State whether the following statement is True or False:
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A bill of ₹ 8,000 drawn on 5th January 2019 for 8 months was discounted for ₹ 7,680 on a certain date. Find the date on which it was discounted at 10% p.a.
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`
