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. - Mathematics and Statistics

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Sum

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.

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Solution

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

Concept: Discount
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Chapter 1: Commission, Brokerage and Discount - Exercise 1.2 [Page 11]

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Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 1 Commission, Brokerage and Discount
Exercise 1.2 | Q 15 | Page 11

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Solution: Banker’s Discount

B.D.= F.V. − C.V. = 8,000 −7,680 = ₹ 320

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∴ B.D. = `("F.V." xx "n"/365 xx "r")/100`

∴ 320 = `(8000 xx "n"/365 xx 10)/100`

∴ n = `square` days

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∴ Date of discounting is `square`


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