Bill Discounting Maths – Multiple Choice Questions -

Last Updated on: 12th December 2024, 03:42 pm

Bill Discounting Maths – MCQ

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Bill Discounting Math MCQ

1.The banker’s discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:
A. Rs. 400
B.Rs. 360
C.Rs. 480
D.Rs. 320
Answer: Option A

Explanation:
$\displaystyle TD=\frac{{B.D.\times 100}}{{100+\left( {R\times T} \right)}}$
$\displaystyle =Rs.\left[ {\frac{{420\times 100}}{{100+\left( {15\times \frac{1}{3}} \right)}}} \right]$
$\displaystyle =Rs.\left( {\frac{{420\times 100}}{{105}}} \right)$
= Rs. 400

2. The banker’s discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is:
A.3 months
B.4 months
C.6 months
D.8 months
Answer: Option B

Explanation:
S.I. on Rs. 1600 = T.D. on Rs. 1680.
$\displaystyle \therefore$ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.
$\displaystyle \therefore Time=\left( {\frac{{100\times 80}}{{Year}}} \right)=\frac{1}{{Year}}=4\text{ months}$

3. The banker’s gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. The present worth is:
A.Rs. 480
B.Rs. 520
C.Rs. 600
D.Rs. 960
Answer: Option C

Explanation:
$\displaystyle T.D.=\left( {\frac{{BG\times 100}}{{Rate\times Time}}} \right)=Rs.\left( {\frac{{24\times 100}}{{10\times 2}}} \right)=Rs.120$
$\displaystyle \therefore P.W.=\frac{{100\times T.D.}}{{Rate\times Time}}=Rs.\left( {\frac{{100\times 120}}{{10\times 2}}} \right)=Rs.600$

4. The banker’s discount on a sum of money for 1 years is Rs. 558 and the true discount on the same sum for 2 years is Rs. 600. The rate percent is:
A.10%
B.13%
C.12%
D.15%
Answer: Option C

Explanation:
B.D. for $\displaystyle \frac{3}{2}$ years=Rs. 558.
B.D. for 2 years $\displaystyle =Rs.\left( {558\times \frac{2}{3}\times 2} \right)=Rs.744$
T.D. for 2 years = Rs. 600.

5. The banker’s gain on a sum due 3 years hence at 12% per annum is Rs. 270. The banker’s discount is:
A.Rs. 960
B.Rs. 840
C.Rs. 1020
D.Rs. 760
Answer: Option C

Explanation:
$\displaystyle T.D.=\left( {\frac{{B.G.\times 100}}{{R\times T}}} \right)=Rs.\left( {\frac{{270\times 100}}{{12\times 3}}} \right)=Rs.750$
B.D. = Rs.(750 + 270) = Rs. 1020.

6. The banker’s discount of a certain sum of money is Rs. 72 and the true discount on the same sum for the same time is Rs. 60. The sum due is:
A.Rs. 360
B.Rs. 432
C.Rs. 540
D.Rs. 1080
Answer: Option A

Explanation:
$\displaystyle Sum=\frac{{B.D\times T.D}}{{B.D.-T.D}}=Rs.\left( {\frac{{72\times 60}}{{72-60}}} \right)=Rs.\left( {\frac{{72\times 60}}{{12}}} \right)=Rs.360$

7. The certain worth of a certain sum due sometime hence is Rs. 1600 and the true discount is Rs. 160. The banker’s gain is:
A.Rs. 20
B.Rs. 24
C.Rs. 16
D.Rs. 12
Answer: Option C

Explanation:
$\displaystyle B.G.=\frac{{{{{\left( {T.D.} \right)}}^{2}}}}{{P.W.}}=Rs.\left( {\frac{{160\times 160}}{{1600}}} \right)=Rs.16$

8. The present worth of a certain bill due sometime hence is Rs. 800 and the true discount is Rs. 36. The banker’s discount is:
A. Rs. 37
B. Rs. 37.62
C. Rs. 34.38
D. Rs. 38.98
Answer: Option B

Explanation:
$\displaystyle B.G.=\frac{{{{{\left( {T.D.} \right)}}^{2}}}}{{P.W.}}=Rs.\left( {\frac{{36\times 36}}{{800}}} \right)=Rs.1.62$
B.D. = (T.D. + B.G.) = Rs. (36 + 1.62) = Rs. 37.62

9. The banker’s gain on a bill due 1 year hence at 12% per annum is Rs. 6. The true discount is:
A.Rs. 72
B.Rs. 36
C.Rs. 54
D.Rs. 50
Answer: Option D

Explanation:
$\displaystyle T.D=\frac{{B.G.\times 100}}{{R\times T}}=Rs.\left( {\frac{{6\times 100}}{{12\times 1}}} \right)=Rs.50$

10. The present worth of a sum due sometime hence is Rs. 576 and the banker’s gain is Rs. 16. The true discount is:
A.Rs. 36
B.Rs. 72
C.Rs. 48
D.Rs. 96
Answer: Option D

Explanation:
T.D. = P.W. x B.G. = 576 x 16 = 96.

11. The true discount on a bill of Rs. 540 is Rs. 90. The banker’s discount is:
A.Rs. 60
B.Rs. 108
C.Rs. 110
D.Rs. 112
Answer: Option B

Explanation:
P.W. = Rs. (540 – 90) = Rs. 450.
S.I. on Rs. 450 = Rs. 90.
$\displaystyle S.I.\text{ }on\text{ Rs}\text{. 540=Rs}\text{.}\left( {\frac{{90}}{{450}}\times 540} \right)=Rs.108$
B.D. = Rs. 108.

12. The banker’s discount on a certain sum due 2 years hence is of the true discount. The rate percent is:
A.11%
B.10%
C.5%
D.5.5%
Answer: Option C

Explanation:
Let T.D. be Re. 1.
$\displaystyle \begin{array}{*{20}{c}} {Then,\text{ }B.D.=Rs.} & {\frac{{11}}{{10}}=} & {Rs.\text{ }1.10.} \end{array}$
$\displaystyle \therefore Sum=Rs.\left( {\frac{{1.10\times 1}}{{1.10-1}}} \right)=Rs.\left( {\frac{{110}}{{10}}} \right)=Rs.11$
S.I. on Rs. 11 for 2 years is Rs. 1.10
$\displaystyle \therefore Rate=Rs.\left( {\frac{{100\times 1.10}}{{11\times 2}}} \right)\%=Rs.5\%$

13. The true discount on a bill of Rs. 2700 is Rs. 200. What is the banker’s discount?
A. Rs. 210
B. Rs. 212
C. Rs. 216
D. Rs. 218
Answer: C

Explanation:
Face value = Rs. 2700
TD = Rs. 200
PW (present worth) = FV (face value) – TD (true discount)
= 2700 ? 200 = Rs. 2500
True discount is the simple interest on the present value for the unexpired time.
Now, simple interest on Rs. 2500 for unexpired time = Rs. 200
$\displaystyle The\text{ }rate\text{ }of\text{ }simple\text{ }interest~=\frac{{200}}{{2500}}\times 100=8\%$
Banker’s discount is the simple interest on the face value of the bill for unexpired time, i.e., simple interest on Rs. 2700 for unexpired time or remaining time.
R = 8%
$\displaystyle =2700\times \frac{8}{{100}}=Rs.216$
Banker’s discount

14. The banker’s discount and the true discount on a sum of money due 8 months hence are 140 and 130 respectively. What are the sum and the rate percent?
A. 1820, 11.5%
B. 1920, 12.5%
C. 1930, 10.5%
D. 1940, 9.5%
Answer: A

Explanation:
Sum = (B.D. * T.D. / B.D. -T.D.)
= (140 * 130) / (140 – 130)
So, the required sum = 18200/10 = Rs. 1820
As B.D. is the S.I. on sum due, so S.I. on Rs. 1820 for 8 months is Rs. 140.
S.I. = Amount * rate of interest * time
140 = 1820 * r * 8/12
140 = 1820 * (r/100) * (2/3)
r = 140 * 100 * 3 / 1820 * 2
= 1050/91 = 11.5 %

15. The present worth or value of a bill due sometime hence is Rs. 1100 and the true discount is Rs. 110. Find the banker’s discount as well as banker’s gain.
A. 132, 16
B. 122, 15
C. 131, 14
D. 121, 11
Answer: D

Explanation:
P.W = 1100
T.D = 110
Sum due = P.W + T.D = 1100 + 110 = 1210
T.D. is the interest on the P.W
Now, interest on 1110 is 110
Now, banker’s discount is the interest on the sum due.
So, interest on 1210 = 110/1100 * 1210 = 121
So, banker’s discount = 121
Now, banker’s gain = banker’s discount – true discount
= 121 – 110 = 11

16. The banker’s gain of a certain sum due 2 years hence at 10% per annum is Rs. 26. Find the present worth.
A. Rs. 450
B. Rs. 550
C. Rs. 650
D. Rs. 750
Answer: C

Explanation:
$\displaystyle T.D.=\frac{{B.G.\times 100}}{{Rate\times Time}}=\frac{{26\times 100}}{{10\times 2}}=Rs.130$
$\displaystyle P.W.=\frac{{100\times T.D}}{{Rate\times Time}}=\frac{{100\times 130}}{{10\times 2}}=Rs.650$

Computation for P.W:
T.D. = 130
Banker Gain = 26
Banker’s Gain = Banker’s Discount – True discount
So, 26 = Banker’s discount – 130
Banker’s discount = 130 + 26 = 156
Now, banker’s discount is the interest on the sum
Let the sum = x
So, 156 = x * (10/100) * 2
156 = x * 0.1 * 2
x = 156 * 10 / 2 = 780
Now, P.W = Sum – T.D
= 780 – 130
= 650

17. The banker’s discount on a certain sum of money is Rs. 88 and the true discount is 77. Find the sum due.
A. Rs. 516
B. Rs. 616
C. Rs. 416
D. Rs. 316
Answer: B

Explanation:
$\displaystyle Sum=\frac{{B.D.\times T.D}}{{B.D-T.D.}}=\frac{{88\times 77}}{{88-77}}=\frac{{6776}}{{11}}=Rs.130$

18. The certain worth of a certain sum due sometime hence is Rs. 1800. If the true discount is Rs. 180, what is the banker’s gain?
A. 18
B. 19
C. 20
D. 21

Answer: A

Explanation:
$\displaystyle B.G.=\frac{{{{{\left( {T.D.} \right)}}^{2}}}}{{P.W.}}$
$\displaystyle =\frac{{180\times 180}}{{1800}}=\frac{{324}}{{18}}=Rs.18$

19. The present worth of a certain bill due sometime hence is Rs. 900 and the true discount is Rs. 45. What is the banker’s discount?
A. Rs. 44.25
B. Rs. 45.25
C. Rs. 46.25
D. Rs. 47.25
Answer: D

Explanation:
$\displaystyle B.G.=\frac{{{{{\left( {T.D.} \right)}}^{2}}}}{{P.W.}}$
$\displaystyle =\frac{{45\times 45}}{{900}}=Rs.2.25$
B.G. = B.D. – T.D.
So, B.D. = B.G. + T.D.
B.D. = 2.25 + 45 = Rs. 47.25

20. If the banker’s gain on a bill due one year hence at 14% per annum is Rs. 8.4, what is the true discount?
A. Rs. 60
B. Rs. 65
C. Rs. 70
D. Rs. 75
Answer: A

Explanation:
$\displaystyle T.D.=\frac{{B.G.\times 100}}{{R\times T}}=\frac{{8.4\times 100}}{{14\times 1}}=\frac{{840}}{{14}}=Rs.60$

21. The banker’s gain on a certain sum due 18 months hence is of the banker’s discount. What is the rate percent?
A. 14.6 %
B. 15.6 %
C. 16.6 %
D. 17.6 %
Answer: C

Explanation:
Let B.D. = Rs. 1
Then, B.G. $\displaystyle =Rs.\frac{5}{{25}}$
T.D.=B.D-B.G. $\displaystyle =1-\frac{5}{{25}}=\frac{4}{5}$
$\displaystyle Sum=\frac{{1\times \frac{4}{5}}}{{1-\frac{4}{5}}}=5$
S.I. on Rs. 4 for 18 months or 1.5 year is Rs. 1.
$\displaystyle Rate=\frac{{100\times 1}}{{4\times 1.5}}=\frac{{20}}{{12}}=16.6\%$

22. If the true discount on a certain sum due 6 months hence at 12% is Rs. 120, find the banker’s discount on the same for the same time and at the same rate.
A. Rs. 127.2
B. Rs. 126.2
C. Rs. 125.2
D. Rs. 124.2
Answer: A

Explanation:
B.G. = S.I. on T.D.
$\displaystyle =120\times \frac{{12}}{{100}}\times \frac{1}{2}=Rs.7.2$
Now, B.G. = B.D. ? T.D. = Rs. 7.2
B.D. = B.G. + T.D
=7.2 + 120 = Rs. 127.2

23. The banker’s discount on Rs. 1500 at 15% per annum is the same as the true discount on Rs. 1550 for the same time and the same rate. What is the time?
A. 0.2 months
B. 0.3 months
C. 0.4 months
D. 0.5 months
Answer: A

Explanation:
As per question:
Bankers Discount, B.D. = Simple Interest on the face value of the bill for unexpired time.
Tue Discount, TD = Simple Interest on the present worth or value for the unexpired time.
S.I. on Rs. 1500 = T.D. on Rs. 1550
Rs. 1500 is the Present Worth or Value of Rs. 1550
Rs. 50 is the simple interest on Rs. 1500 at 15%
$\displaystyle So,\text{ }50=\frac{{1500\times T\times 15}}{{100}}$
$\displaystyle 50=15\times T\times 15$
$\displaystyle T=\frac{{50}}{{225}}=\frac{2}{9}=0.2\text{ months}$

24. The bankers gain on a sum due 5 years hence at 14% per annum is Rs. 280. What is the banker’s discount?
A. Rs. 780
B. Rs. 680
C. Rs. 580
D. Rs. 480
Answer: B

Explanation:
$\displaystyle \text{T}\text{.D}\text{.=}\frac{{B.G.\times 100}}{{R\times T}}$
$\displaystyle =\frac{{280\times 100}}{{14\times 5}}=Rs.400$
B.G. = Bankers discount – True discount
B.D. = B.G. + True discount
= 280 + 400
= Rs. 680

25. The B.G. on a certain sum 4 years hence at 5% is Rs. 400. Find the present worth.
A. Rs.10000
B. Rs.10500
C. Rs.11000
D. Rs.11500
Answer: A

Explanation:
$\displaystyle \text{T}\text{.D}\text{.=}\frac{{B.G.\times 100}}{{R\times T}}$
$\displaystyle =\frac{{400\times 100}}{{5\times 4}}=Rs.2000$
$\displaystyle T.D.=\sqrt{{PW\times BG}}$
$\displaystyle 2000=\sqrt{{PW\times 400}}$
$\displaystyle 4000000=PW\times 400$
$\displaystyle P.W.=\frac{{4000000}}{{400}}=Rs.10000$

26. The present worth of a certain bill due sometime hence is Rs. 450. If the true discount is Rs. 15, what is the banker’s discount?
A. Rs. 12.5
B. Rs. 13.5
C. Rs. 14.5
D. Rs. 15.5
Answer: D

Explanation:
$\displaystyle B.G.=\frac{{{{{\left( {T.D.} \right)}}^{2}}}}{{P.W.}}$
$\displaystyle =\frac{{{{{\left( {15} \right)}}^{2}}}}{{450}}$
$\displaystyle =\frac{{225}}{{450}}=Rs.0.5$
B.G. = B.D. – T.D.
0.5 = B.D. – 15
B.D. = 0.5 + 15 = Rs. 15.5

27. A bill is discounted at 20% per annum. If the banker’s discount is allowed, at what rate percent should be proceeds be invested so that nothing will be lost?
A. 25%
B. 35%
C. 45%
D. 55%
Answer: A
Explanation:
Let the amount = Rs. 100
So, B.D. = Rs. 20 as banker’s discount is the simple interest on the face value of the bill for the unexpired time and bill is discounted at 20% per annum.
Proceeds = Rs. 100 – Rs. 20 = Rs. 80
So, we should get Rs. 20 as the interest of Rs. 80 for one year so that nothing will be lost.
$\displaystyle 20=\frac{{80\times 1\times R}}{{100}}$
$\displaystyle R=\frac{{2000}}{{80}}=25\%$

28. A bill of Rs. 105400 due in 6 months is discounted at 9% per annum. The Banker’s Discount is:
a) 4500
b) 4743
c) 4850
d) 4900
Ans (b)
Explanation:
Bankers discount BD = (F X T XR) /100
Here, F = Rs. 105400, T = 6/12 years = 1/2 year, R = 9%
BD = (F X T X R)/100 = (105400 x 1/2 x 9)/100
1054 x (1/2) x 9 = 4743.

29. The true discount on a bill of Rs. 2700 is Rs. 200. Banker’s discount is

Rs. 210
Rs. 212
Rs. 216
Rs. 218

Ans. (c)
Explanation:
Face value = Rs. 2700, TD = Rs. 200
PV (Present Value) = FV (face value) – TD (true discount) = 2700 – 200 = Rs. 2500
First we have to compute the Simple Rate of Interest from the given data.
Interest Amount on 2500 is 200. So, Interest Rate is = (200/2500) = .08 = 8/100 = 8%
Banker’s discount is the simple interest on the face value of the bill for unexpired time,
Simple interest on Rs. 2700 at 8% = 2700 x .08= 216

30. A Bill is due 8 months. The Banker’s Discount is 140 and True Discount is 130. The Bill Amount is

1820
1920
1930
1940

Ans: (a)
Explanation:
Here Bankers Discount BD=140. True Discount TD=130
Bill Amount = (B.D. * T.D. / (B.D. -T.D.)
= (140 * 130) / (140 – 130) = 18200/10 = Rs. 1820

31. A Bill is due 8 months. The Banker’s Discount is 140 and True Discount is 130. The Interest Rate is :

11
11.5
12
12.25

Ans: (b)
Explanation:
First, we have to calculate Bill Amount
Bill Amount = (B.D. * T.D. / (B.D. -T.D.)
= (140 * 130) / (140 – 130) = 18200/10 = Rs. 1820
Next we have to Calculate Interest rate (r)
Interest = Amount X rate X Time. Here Bill Amount is 1820, Time = 8/12 years
Bankers Discount is the Interest Amount on Bill = 140
So, 140 = 1820 X r X 8/12
140 = 1820 X (r/100) X (2/3)
r = (140 X 100 X 3) / (1820 X 2) = 42000 / 3640=1050/91= 11.5 %

32. The Present Value of a Bill is Rs. 1800, If the True Discount Rs. 180. Then banker’s gain is:

a) 17
b)18
c) 19
d)20
Ans: (b)
Banker’s gain BG=TD²/ PV = (180)²/1800 = (180 X 180) / 1800 = 180/10=18

33. The present value of a certain is Rs. 900 and the True Discount is Rs. 45. Banker’s discount is :

Rs. 44.25
Rs. 45.25
Rs. 46.25
Rs. 47.25

Ans: (d)
Explanation:
Bakers Gain BG= (True Discount)² / Present Value
= (45 X 45) / 900 = 2.25
So, Bankers Discount = True Discount + Bankers Gain= 45+2.25= 47.25

34. A Bill is discounted at 20% per annum and the fund reinvested. What should be the minimum Interest rate of Investment so there is no gain no loss.

Ans: (a)
Banker’s Discount is the simple interest on the face value of the bill
On Rs. 100, banker’s discount @20% = Rs. 20. So, Bank will give 100-20=80
So, we should get Rs. 20 as the interest of Rs. 80 for one year so that nothing will be lost.
I=FXTXR/100. So, 20=80X1XR/100. Or, 80R=2000, or R=2000/80=25%

35. The banker’s discount on Rs. 1500 at 15% per annum is the same as the true discount on Rs. 1550 for the same time and the same rate. The Bill Due period is :

Ans: (a)
Explanation:
Bankers Discount, B.D. = Simple Interest on the face value of the bill.
Tue Discount, TD = Simple Interest on the present value of the bill.
So, 1500 is the present value of 1550 Bill Value. So, True Discount is 1550-1500=50
Simple Interest. on Rs. 1500 = 1500XTX 15
So, (1500XTX 15)/100 = 50. Or, 225 X T=50, or, T= 50/225 = 2/9

36. The Present Value of a bill is Rs. 450. If the true discount is Rs. 15, what is the banker’s discount?

Rs. 12.5
Rs. 13.5
Rs. 14.5
Rs. 15.5

Ans: (d)
Explanation:
Banker Gain BG=TD²/ PV, or, BG=(15)²/450 = 225/450=.50
BG = BD-TD. Or .50=BD-15, or BD=.50+15=15.50

Bill Discounting Maths – Multiple Choice Questions

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