Banker’s Discount Problems Quiz 4
Q1. 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
Explanation:
T.D. = B.D. x 100/100 + (R x T)
= 420 * 100 / 100+ {15*1/3}
= Rs. 420 * 100 /105
= Rs. 400
Q2. 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
Explanation:
S.I. on Rs. 1600 = T.D. on Rs. 1680.
Rs. 1600 is the P.W. of Rs. 1680,
i.e., Rs. 80 is on Rs. 1600 at 15%.
Time = 100 * 80/ 1600*15 Year
= 1/3 year
= 4months.
Q3. 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
Q4. The banker’s gain on a certain sum due 1(1/2) years hence is 3/25 of the banker’s discount.The rate percent is :
A. 5(1/5)%
B. 9(1/9)%
C. 8(1/8)%
D. 6(1/6)%
Q5. 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
Q6. 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
Explanation:
B.G. = (T.D.)2
P.W. = Rs. 36*36/800
= Rs. 1.62
Therefore; B.D. = (T.D. + B.G.)
= Rs. (36 + 1.62)
= Rs. 37.62
Q7. The banker’s discount on Rs. 1800 at 12% per annum is equal to the true discount on Rs. 1872 for the same time at the same rate. Find the time.
A) 7 months
B) 6 months
C) 3 months
D) 4 months
Explanation:
S.I. on Rs. 1800 = T.D. on Rs. 1872.
P.W. of Rs. 1872 is Rs. 1800.
Rs. 72 is S.I. on Rs. 1800 at 12%.
Time =[(100 x 72)/ (12×1800)]year
=1/3year
= 4 months.
Q8. The B.G. on a certain sum 4 years hence at 5% is Rs. 200. What is the present worth?
A) Rs. 4500
B) Rs. 6000
C) Rs. 5000
D) Rs. 4000
Explanation:
T = 4 years
R = 5%
Banker’s Gain,
BG = Rs.200
Now, by applying TD formulae
PW = 1000000/200= 5000
Q9. A bill for Rs. 6000 is drawn on July 14 at 5 months. It is discounted on 5th October at 10%. Find the banker’s discount, true discount, banker’s gain and the money that the holder of the bill receives.
A) 4390
B) 6580
C) 5880
D) 5350
Explanation:
Face value of the bill = Rs. 6000.
Date on which the bill was drawn = July 14 at 5 months.
Nominally due date = December 14.
Legally due date = December 17.
Date on which the bill was discounted = October 5.
Unexpired time : Oct. Nov. Dec.
26 + 30 + 17 = 73 days =1/ 5Years.
B.D. = S.I. on Rs. 6000 for 1/5 year
= Rs. (6000 x 10 x1/5 x1/100)
= Rs. 120.T.D. = Rs.[(6000 x 10 x1/5)/(100+(10*1/5))]
=Rs.(12000/102)
=Rs. 117.64. B.G.
= (B.D.) – (T.D.)
= Rs. (120 – 117.64)
= Rs. 2.36.
Money received by the holder of the bill = Rs. (6000 – 120)
= Rs. 5880.
Q10. If the true discount on a certain sum due 6 months hence at 15% is Rs. 120, what is the banker’s discount on the same sum for the same time and at the same rate?
A) 50
B) 129
C) 100
D) 160
Explanation:
B.G. = S.I. on T.D.
= Rs.(120 x 15 x 1/2 x 1/100)
= Rs. 9. (B.D.) – (T.D.)
= Rs. 9. B.D.
= Rs. (120 + 9)
= Rs. 129.