**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

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

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:**

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.

- Rs. 516
- Rs. 616
- Rs. 416
- Rs. 316

**Answer:** B

**Explanation:**