Question 1

Question 1: What is the present worth of a sum of ₹ 10,920 due six months hence at 8% p.a simple interest?

Accepted Answer

Given, SD = ₹ 10,920 n = year = year r = 8% We have, Thus the present worth is ₹ 10,500

Question 2

Question 2: What is the sum due of ₹ 8,000 due 4 months at 12.5% simple interest?

Accepted Answer

Given, PW = ₹ 8,000, n = year = year, r = 12.5% We have, Thus, the sum due is ₹ 8,333.33

Question 3

Question 3: The true discount on the sum due 8 months hence at 12% p.a. is ₹ 560. Find the sum due and present worth of the bill.

Accepted Answer

Given, TD = ₹ 560, n = year = year, r = 12% We have, TD = ∴ 560 = ∴ PW = 560 × = ₹ 7,000 Now, SD = PW + TD = 7,000 + 560 = ₹ 7,560

Question 4

Question 4: The true discount on a sum is of the sum due at 12% p.a. Find the period of the bill.

Accepted Answer

8 × n × 12 = 3(100 + n × 12) 96n = 300 + 36n 60n = 300 ∴ n = 5 ∴ Period of the bill = 5 years.

Question 5

Question 5: 20 copies of a book can be purchased for a certain sum payable at the end of 6 months and 21 copies for the same sum in ready cash. Find the rate of interest.

Accepted Answer

Given, n = year = year Let the sum payable be ₹ x Let the rate of interest be r% According to given condition, PW of one book = SD of one book = Thus, the rate of interest is 10%.

Question 6

Question 6: 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.

Accepted Answer

And, Banker’s Gain (BG) = BD – TD = 190.80 – 182.58 = ₹ 8.22

Question 7

Question 7: The true discount on a bill is ₹ 2,200 and bankers discount is ₹ 2,310. If the bill is due 10 months, hence, find the rate of interest.

Accepted Answer

Given, TD = ₹ 2,200, BD = ₹ 2,310 n = year ∴ ∴ r = 6% Thus, rate of interest is 6%

Question 8

Question 8: A bill of ₹ 6,395 drawn on 19th January 2015 for 8 months was discounted on 28th February 2015 at 8% p.a. interest. What is the banker’s discount? What is the cash value of the bil

Accepted Answer

Face value = ₹ 6,395 Date of drawing = 19/01/2015 Period of the bill = 8 months Nominal Due date = 19/09/2015 Legal due date = 22/09/2015 Date of discounting = 28/02/2015 Now, the unexpired period = Legal due date – Date of discounting = 22/09/2015 – 28/02/2015 = days (as shown below) Cash Value = F

Question 9

Question 9: A bill of ₹ 8,000 drawn on 5th January 1998 for 8 months was discounted for ₹ 7,680 on a certain date. Find the date on which it was discounted at 10% p.a.

Accepted Answer

Bankers discount (BD) = FV – cash value = 8,000 – 7,680 = ₹ 320 Let the unexpired period be x days ∴ BD = ∴ 320 = ∴ x = 146 days ∴ The unexpired days = 146 days Date of drawing = 05/01/1998 Period of bill = 8 months Nominal due date = 05/09/1998 Legal due date = 08/09/1998 Thus, the date of discount

Question 10

Question 10: A bill drawn on 5th June for 6 months was discounted at the rate of 5% p.a. on 19th October. If the cash value of the bill is ₹ 43,500, find the face value of the bill.

Accepted Answer

Date of drawing = 5th June Period of bill = 6 months Nominal due date = 5th December Legal due date = 8th December Date of discounting = 19th October Rate of interest = 5% p.a. Let the face value of the bill be ₹ x The unexpired period

Question 11

Question 11: A bill was drawn on 14th April for ₹ 7,000 and was discounted on 6th July at 5% p.a. The Banker paid ₹ 6,930 for the bill. Find the period of the bill.

Accepted Answer

Face value = ₹ 7,000, cash value = ₹ 6,930 ∴ Banker’s discount = 7,000 – 6,930 = ₹ 70 Date of drawing = 14/04 Date of discounting = 06/07 Rate of interest = 5% Let the unexpired period = x days ∴ BD = ∴ 70 = ∴ x = 73 days ∴ Legal due date of the bill is 73 days after the date of discounting. ∴ Legal

Question 12

Question 12: If the difference between true discount and banker’s discount on a sum due 4 months hence is ₹ 20. Find true discount, banker’s discount and amount of bill, the rate of simple inte

Accepted Answer

Banker’s gain (BG) = Banker’s discount (BD) – True Discount (TD) ∴ BG = ₹ 20 Also, BG = ∴ 20 = ∴ 20 = ∴ TD = ₹ 1200 Now, BD = BG + TD = 20 + 1,200 = ₹ 1,220 Also, BD = ∴ 1,220 = ∴ FV = 1,200 × 60 = ₹ 73,200 ∴ Amounting the bill = ₹ 73,200

Question 13

Question 13: 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.

Accepted Answer

Face Value = ₹ 51,000 Date of drawing = 18/02/2010 Period of the bill = 9 months Nominal due date = 18/11/2010 Legal due date = 21/11/2010 Date of discounting = 28/06/2010 Unexpired period ∴ TD = ₹ 1,000 ∴ BG = BD – TD = 1,020 – 1,000 = ₹ 20

Question 14

Question 14: A certain sum due 3 months hence is of the present worth, what is the rate of interest.

Accepted Answer

Step-by-step solution provided.

Question 15

Question 15: 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.

Accepted Answer

Date drawing = 28/02/2007 Period of the bill = 8 months Nominal due date = 28/10/2007 Legal due date = 31/10/2007 Date of discounting = 26/03/2007 Cash value = ₹ 10,992 Rate of interest = 14% Let face value of the bill = ₹ x Bankers discount = Face value – Cash value = x – 10,992 Also, Banker s disc

Chapter 1 Commission, Brokerage and Discount Ex 1.2 Solutions