Aptitude True Discount and Banker's Discount Concepts

Aptitude True Discount and Banker's Discount Test Paper 1

1) The true discount on a bill of Rs. 2700 is Rs. 200. What is the banker's discount?

Rs. 210
Rs. 212
Rs. 216
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
The rate of simple interest Apti True Discount and Banker's Discount

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%
Banker's discount Apti True Discount and Banker's Discount

2) 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?

1820, 11.5%
1920, 12.5%
1930, 10.5%
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 %

3) 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.

132, 16
122, 15
131, 14
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

4) The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 26. Find the present worth.

Rs. 450
Rs. 550
Rs. 650
Rs. 750

Answer: C

Explanation:

Apti True Discount and Banker's Discount

Solution 2 for P.W:
T.D. = 130
Banker Gain = 26
Banker's Gain = Banker's Discount - True discount
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

5) The banker's discount on a certain sum of money is Rs. 88 and the true discount is 77. Find the sum due.