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प्रश्न
A bill of a certain sum drawn on 28th February 2007 for 8 months was encashed on 26th March 2007 for ₹ 10,992 at 14% p.a. Find the face value of the bill.
उत्तर
We know that,
Banker’s discount (B.D.) = face value – cash value
∴ B.D. = F.V. – 10,992 …(i)
Date of bill drawn = 28th February 2007
Date of bill discounting = 26th March 2007
Period of bill = 8 months
Nominal due date = 28th October 2007
Legal due date = 31st October 2007
Number of days from date of bill discounting to legal due date
| Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Total |
| 5 | 30 | 31 | 30 | 31 | 31 | 30 | 31 | 219 days |
∴ n = `219/365 = 3/5`
Since,
Banker’s discount = `("F.V." xx "n" xx "r")/100`
∴ F.V. – 10,992 = `("F.V." xx 3/5 xx 14)/100` ....…[From (i)]
∴ F.V. – 10,992 = `("F.V." xx 3 xx 14)/(100 xx 5)`
∴ F.V. – `(42 "F.V.")/500` = 10,992
∴ `(500 "F.V." - 42 "F.V.")/500 = 10,992`
∴ `(458 "F.V.")/500 = 10,992`
∴ F.V. = `10992 xx 500/458`
∴ F.V. = 12000
∴ Face value of the bill is ₹ 12,000
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The sum due is also called as ______.
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The banker’s discount is also called _______.
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The date by which the buyer is legally allowed to pay the amount is known as _______.
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State whether the following statement is True or False.
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The difference between true discount and banker’s discount on 6 months hence at 4% p.a. is ₹ 80. Find the true discount, banker’s discount and amount of the bill.
The date on which the bill is drawn is called as ______
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`
The banker’s discount is also called true discount.
