Q 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 - A

Explanation

"T.D.
=(B.D. x 100)/100 + (R x T)
= Rs.(420 x 100)/(100 +15 x(1/3))

= Rs.(420 x 100)/105
= Rs. 400.
"```

Q 2-The bankers discount and true discount on a sum of money due 8 months hence are Rs.180 & Rs.80 resp. Find the sum

A - 122

B - 124

C - 136

D - 144

```Answer - D

Explanation

Sum = (B.D * T.D) / (B.D) -(T.D) = (180 * 80) / (180 -80) = 144```

Q 3-The banker's discount on Rs. 1650 due a certain time hence is Rs. 165. Find the banker's gain.

A - 10

B - 15

C - 20

D - 25

```Answer - B

Explanation

"Sum = [(B.D.xT.D.)/ (B.D.-T.D.)] = [(B.D.xT.D.)/B.G.]
T.D./B.G. = Sum/ B.D. =1650/165 =10/1
Thus, if B.G. is Re 1, T.D. = Rs. 10.
If B.D.is Rs. ll, T.D.=Rs. 10.
If B.D. is Rs. 165, T.D. = Rs. [(10/11)xl65] =Rs.150
And, B.G. = Rs. (165 - 150) = Rs, 15."```

Q 4-If the discount on Rs. 498 at 5% simple interest is Rs.18, when is the sum due?

A - 8 months

B - 11 months

C - 10 months

D - 9 months

```Answer - D

Explanation

"F = Rs. 498 TD = Rs. 18
PW = F - TD = 498 - 18 = Rs. 480
R = 5% TD = (PW × TR)/100
⇒18=(480× T ×5)/100 ⇒18=24×T
⇒ T =18/24=3/4 years=12×(3/4) months
= 9 months
"```

Q 5-The banker's discount calculated for one year is 21 times of his gain. Find the rate of interest?

A - 7%

B - 6%

C - 4%

D - None

```Answer - D

Explanation

"The rate of interest for the bankers discount is 5%.
Solution: Formula for Bankers gain: Banker's Gain
(B.G.) = (B.D.) - (T.D.) T.D = (B.G. x 100)/(Rate x Time)
Bankers discount calculated for one year is 21 times of his gain.
B.D = 21 * B.G Time = 1 year So, B.G = [(21 * B.G) - (B.G. x 100)/(Rate x 1)]
= 21B.G - (100B.G)/rate B.G * rate
= 21B.G * rate - 100B.G 20B.G * rate = 100B.
G rate = 100B.G/20B.G rate = 5%
Hence, the rate of interest for the bankers discount is 5%
"```

Q 6-The present worth of a sum due sometime hence is Rs. 576 and the bankers gain is Rs. 16. The true discount is:

A - Rs. 36

B - Rs. 72

C - Rs. 48

D - Rs. 96

```Answer - D

Explanation

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

Q 7-The bankers gain on a certain sum due 1 1212 years hence is 3/25 of the bankers discount. The rate percent is

A - 26/5%

B - 100/9%

C - 65/8%

D - 37/6%

```Answer - B

Explanation

"Let, B.D = Re. 1.
Then, B.G. = Re.3/25
So, T.D. = (B.D. - B.G.) = Re. (1−(3/25))=Re.22/25.
Sum (1×(22/25)/(1−(22/25)))=Rs.223(1×(22/25)/1−(22/25))=Rs.223
S.I. on Rs. 22/3 for 3/2 years is Re.1.
So , Rate = (100×1)/(22/3)×(3/2)) % = 100/9%
"```

Q 8-The bankers 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 - A

Explanation

"Sum = (B.D.×T.D)/(.B.D.−T.D.)
=Rs.(72×60)/(72−60)=Rs.(72×60)/60)=Rs.360.
"```

Q 9-If the true discount on s sum due 2 years hence at 14% per annum be Rs. 168, the sum due is:

A - Rs. 768

B - Rs. 968

C - Rs. 1960

D - Rs. 2400

```Answer - A

Explanation

"P.W. = (100×T.D.)/(R×T)=(100×168)/14×2=600..
So, Sum = (P.W. + T.D.) = Rs. (600 + 168) = Rs. 768."```

Q 10-The present worth of Rs. 1404 due in two equal half-yearly installments at 8% per annum simple interest is:

A - Rs. 1325

B - Rs. 1300

C - Rs. 1350

D - Rs. 1500

```Answer - A

Explanation

"Required sum = P.W. of Rs. 702 due 6 months + P.W. of Rs. 702 due 1 year hence
= Rs. [(100×702100+8×12)+(100×702100+(8×1))][(100×702100+8×12)+(100×702100+(8×1))]
= Rs. (675 + 650)
= Rs. 1325."```

Q 11-The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum is:

A - Rs. 1800

B - Rs. 1450

C - Rs. 1360

D - Rs. 6800

```Answer - C

Explanation

Sum = (S.I×T.D)/((S.I.)−(T.D.))=(85×80)/(85−80)=Rs.1360```

Q 12-The interest on Rs. 750 for 2 years is the same as the true discount on Rs. 960 due 2 years hence. If the rate of interest is the same in both cases, it is:

A - 12%

B - 14%

C - 15%

D - 50/3%

```Answer - B

Explanation

"S.I. on Rs. 750 = T.D. on Rs. 960.
This means P.W. of Rs. 960 due 2 years hence is Rs. 750.
So,  T.D. = Rs. (960 - 750) = Rs. 210.
Thus, S.I. on R.s 750 for 2 years is Rs. 210.
So, Rate =    (100×210)/(750×2)  %  = 14%"```

Q 13-Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?

A - Rs. 10

B - Rs. 10.40

C - Rs. 15.20

D - Rs. 13

```Answer - B

Explanation

"S.I. on Rs. (260 - 20) for a given time = Rs. 20.
S.I. on Rs. 240 for half the time = Rs. 10.
T.D. on Rs. 250 = Rs. 10.
Therefore T.D. on Rs. 260 = Rs. ((10/250)×260)=Rs.10.40"```

Q 14-The present worth of Rs. 2310 due 5/2 years hence, the rate of interest being 15% per annum, is :

A - Rs. 1750

B - Rs. 1680

C - Rs. 1840

D - Rs. 1443.75

```Answer - B

Explanation

P.W. = Rs. [100×2310)/(100+(15×(5/2))]=Rs.1680.```

Q 15-The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is:

A - 6 months

B - 8 months

C - 9 months

D - 10 months

```Answer - D

Explanation

"P.W. = Rs. (1760 -160) = Rs. 1600.
So, S.I. on Rs. 1600 at 12% is Rs. 160.
Therefore Time = (100×160)/(1600×12))=5/6years
=((5/6)×12)months=10months.
"```