2nd PUC Basic Maths Question Bank Chapter 8 Bill Discounting Ex 8.1

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Karnataka 2nd PUC Basic Maths Question Bank Chapter 8 Bill Discounting Ex 8.1

Part – A and B

2nd PUC Basic Maths Bill Discounting Ex 8.1 One or Two Marks Questions with Answers

Question 1.
A bill was drawn on 14-3-2013 for 3 months. When does the bill fall legally due?
Answer:
L.D.D = DD + BP + 3 days

∴L.D.D is 17^th June 2013

Question 2.
A bill drawn for 3 months was legally due on 18-8-2012. Find the date of drawing of the bill.
Answer:
Drawn date = L.D.D – Bill period – 3days grace = 14 – 3 – 2013
= 18 – 8 – 2012

∴ Drawn date is 15^th May 2012

Question 3.
Find the present value of ₹ 750 due 4 months hence at 15% p.a.
Answer:
Given
F = 750, T = 4 months = \(\frac{4}{12}\), r= 15% = 0.15.

Question 4.
Find the banker’s discount on a bill of ₹ 415 due 9 months hence at 15% p.a.
Answer:
Given
F = 415, t = \(\frac{9}{12}\) year,
r = 15% = 0.15
B.D = Ftr = 415 x \(\frac{9}{12}\) × 0.15= 46.68.

Question 5.
Define Banker’s Gain.
Answer:
Banker gain is difference between BD & TD i.e., BG = BD – TD

Question 6.
Define Banker’s Discount.
Answer:
Banker’s Discount is the Simple interest calculated by the banker on the face value of the bill i.e., BD = Ftr

Question 7.
Find the present value of 2320, due 2 years hence, at 8% per annum.
Answer:
Given F= 2320,t = 2years, r = 0.08, P = ?

Question 8.
Find the BD on ₹ 1015, payable after 3 months at 6% p.a.
Answer:
Given
F = 1015,
F=1015, t = \(\frac{3}{12}\) year, r = \(\frac{6}{100}\) = 0.06, BD = ?
BD = Ftr = 1015 x \(\frac{3}{12}\) × 0.06 = 15.22

Question 9.
Find the true discount on ₹ 1380, due 1\(\frac{1}{2}\) years after, at 10% p.a.
Answer:
Given
F = ₹ 1380, t = \(\frac{3}{2}\) year , r = 10% = 0.1.

Question 10.
TD on a bill was ₹ 100 and BG was ₹ 10. What is the face value of the bill?
Answer:
Given TD = 100, BG = 10, F = ?
BD = TD + BG = 100 + 10 = 110

Question 11.
A banker pays ₹ 2380 on a bill of ₹ 2500, 73 days before the legal due date. Find the rate of discount charged by the banker.
Answer:
Given Discounted value = 2380, F = 2500
t = \(\frac{73}{365}=\frac{1}{5}\) year , r = ?
D.V. = F(1 – tr)
2380 = 2500 \(\left(1-\frac{1}{5} r\right)\)
\(\frac{2380}{2500}=\left(1-\frac{r}{5}\right)\)
0.952 = 1 – \(\frac{r}{5}\)
\(\frac{r}{5}\) = 1 – 0.952 = 0.048
∴ r = 5 × 0.048 = 0.24 × 100 = 24%

Question 12.
The Banker’s discount and true discount on a sum of money due 3 months hence are ₹ 154.50 and ₹ 150 respectively. Find the sum of money and the rate of interest.
Answer:
Given BD = 154.5, t = \(\frac{3}{12}\) , TD = 150, t = ? r = ?

Question 13.
BD and BG on a certain bill due after sometime are 1250 and 350 respectively. Find the face value of the bill.
Answer:
BD and BG on a
Given
BD = 1250, BG = 50, F = ?
BG = BD – TD
TD = BD – BG = 1250 – 50 = 1200

Part – C

2nd PUC Basic Maths Bill Discounting Ex 8.1 Three or Four Mark Questions with Answers

Question 1.
The difference between banker’s discount and true discount on a bill due after 6 months at 4% interest p.a. is ₹ 20. Find the true discount, banker’s discount and face value of the bill.
Answer:
Given
BG = ₹ 20, r = 4% = 0.04, t = 6 Months = \(\frac{6}{12}=\frac{1}{2}\)
TD = ?, BD = ?, F = ?
W.K.T. = BG = TD. tr
20 = TD \(\frac{1}{2}\) x 0.04
40 = 0.04 TD ⇒ TD = \(\frac{40}{0.04}\) = ₹ 1000
BD = BG + TD; = 20 + 1000 = 1020

Question 2.
The BG on a certain bill due 6 months hence is ₹ 10, the rate of interest being 10% p.a. find the face value of the bill and the true present value.
Answer:
BG = 10, ⇒ BD – TD = 10,t = \(\frac{6}{12}=\frac{1}{2}\)year, r= 10% = 0.1, F = ? P = ?
BG = TD.tr
10 = TD × \(\frac{1}{2}\) × 0.1
TD = \(\frac{20}{0.1}\) = 200 ;
BD = TD + BG = 200 + 10 = 210.

Question 3.
A banker discounts a bill for a certain amount having 32 days to run before it matures at 15% p.a. The discounted value of the bill is ₹ 995.90. What is the face value of the bill, banker’s discount, true discount and banker’s gain?
Answer:
Given t = \(\frac{32}{365}\) year, r = 0.15, D.V = ₹995.90, F = ?, BD = ?, TD = ?, BG = ?
Discounted Value = F(1 – tr), 995.90 = F ( 1 – \( \frac{32}{365}\) × 0.05)

D= F – Discounted Value;
= 1009.017 – 995.90 = 13.117

BG = BD – TD = 13.117 – 12.948 = 0.169

Question 4.
A bill for ₹ 14,600 drawn at 3 months after date was discounted on 11-11-99 for ₹ 14,320. If the discount rate is 20% p.a. on what date was the bill drawn?
Answer:
Given DV = 14320, F = 14,600, r=0.2,
DD = ?
W.K. Discounted value = F(1 – tr)
14320 14,320 = 14,600 (1 – 0.2t);
\(\frac{14320}{14600}\) = 1-0.2t
t = 0.1 year = 0.1 ~ 365 = 36 days
L.D.D = 36 days + 11-11-99 = Dec. 17
Drawn date = L.D.D – BP – 3 grace days

∴Bill was drawn on October 14th 3

Question 5.
A bill for ₹ 2920 was drawn on September 11 for 3 months after date and was discounted at 16% p.a. for ₹ 2875.20. On what date was the bill discounted?
Answer:
Given drawn date = 11^th Sep., F = 2920, DV = 2875.20, r = 0.16
BD = F – Discounted value
= 2920 – 2875.20
BD = 44.8
& BD = Ftr.
44.8 = 2920 × 0.16 × t

t = \(\frac{44.8}{2920 \times 0.16}\) = 0.0958 years = 0.0958 × 365 = 35 days
Discounted date = L.D.D – Discount period = Dec. 14^th – 35 days = 9^th November

Question 6.
A bill for ₹ 3500 due for 3 months was drawn on 27 march 2012 and was discounted on 18 April 2012, at the rate of 7% p.a. Find the banker’s discount and discounted value of the bill.
Answer:
Given
F = 3500, r = 0.07, B.P = 3 Months
DD = 27th March 2012, Discounted on 18^th April 2012; BD = ?, DV = ?
L.D.D = DD + BD + 3 grace days

t = No. of days from April 18th to 30th June
12 + 31 + 30 = 73 days =\(\frac{73}{365}\) Year
DV = F(1 – tr) = 3500 1 – \(\frac{73}{365}\) x 0.07)
DV = 3451.00;
BD = F – DV = 3500 – 3451 = ₹ 49

Question 7.
A bill for 12900 was drawn on 3 Feb 2004 at 6 months and discounted on 13 March 2004 at 8% p.a. For what sum was the bill discounted and how much did the banker gain in this transaction?
Answer:
Given
F = 12900, r = 0.08, BG = ?
L.D.D = DD + BP + 3days

t = No. of days from discounted date till LDD = 13 – 3 – 200 to 6 – 8 – 2004
Mar. + Apr. + May + June + July + Aug
= 18 + 30 + 31 + 30 + 31 + 6 = 146 days = \(\frac{146}{865}\)
∴OV = F(1 – tr)
= 12900 (1 – \(\frac{146}{365}\) x 0.08
= 12900 (1 -0.032)
DV = 12487.2
BD = F – Discounted value
= 12900 – 12487.2 = 412.8
TD = \(\frac{B D}{1+t r}=\frac{412.8}{1+0.032}\) = 400
BG = BD – TD = 412.8 – 400 = ₹ 12.8

Question 8.
The banker’s gain on a bill is \(\frac{1}{9}\) th of the banker’s discount, rate of interest being 10% p.a. Find the unexpired period of the bill.
Answer:
Given BG = \(\frac{1}{9}\)BD & r= 0.1
9(BD – TD) = BD
8BD = 9TD
BD 8BD=9. \(\frac{\mathrm{BD}}{1+\mathrm{tr} \mathrm{r}}\)
1+ tr = \(\frac{9}{8}\) = 1.125
tr = 1.125 – 1
t(0.1) = 0.125
t = \(\frac{0.125}{0.1}\) = 1.25years
t = 1.25 × 12 = 15 months

Question 9.
A bill for ₹ 2725.25 was drawn on 03-06-2010 and made payable 3 months after due date. It was discounted on 15-6-2010 at 16% per annum. What is the discounted value of the bill and how much did the banker gain?
Answer:
Given F = 2725.25, r = 0.16, DV = ?, BG = ?, DD = 03-6-2010, BP = 3 months
∴ L.D.D = DD + BD + 3days
= 6-9-2010.
t = No. of days from 15^th June to 6^th Sept = June + July + August + September
= 15 +31 +31 + 6 = 83 days = \(\frac{83}{365}\) years
Discounted value = F (1 – tr)
= 2725.25 (1 – \(\frac{83}{365}\) × 0.16 = 2725.25 (1 – 0.036)
DV = 2627.14
BD = F – Discounted value = 2725.25 – 2627.14 = 98.10
TD = \(\frac{B D}{1+t r}=\frac{98.10}{1.036}\) = 94.69
BG = BD – TD = 98.10 – 94.69 = 3.41