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QUESTION: 1

The banker's gain of a certain sum due 3 years hence at 10% per annum is Rs. 36. What is the present worth ?

Solution:

T = 3year

R = 10%

TD = (BG × 100)/TR

= (36 × 100)/(3 × 10)

= 12 × 10

= Rs.120

TD = (PW × TR)/100

⇒ 120 = (PW × 3 × 10)/100

⇒ 1200 = PW × 3

PW = 1200/3

= Rs.400

QUESTION: 2

The present worth of a certain sum due sometime hence is Rs. 3400 and the true discount is Rs. 340. The banker's gain is:

Solution:

BG = (TD)^{2}/PW

= (340)2/3400

= (340×340)/3400

= 340/10

= Rs.34

QUESTION: 3

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. What is the time?

Solution:

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)

= 1/3 year

= 4 months.

QUESTION: 4

The banker's gain on a certain sum due 5/2 years hence is 9/25 of the banker's discount. What is the rate percent?

Solution:

Let BD = 1

Then, BG = 9/25

T = 5/2 years

TD = BD - BG

=> 1 - 9/25

=> 16/25

BG = (TD * RT)/100

9/25 = 16/25 * R * 5/2 * 1/100

R = 45/2

R = 22 1/2

QUESTION: 5

The banker's gain on a sum due 3 years hence at 12% per annum is Rs. 360. The banker's discount is:

Solution:

BG = Rs. 360

T = 3 years

R = 12%

TD = (BG×100)/TR

= (360×100)/(3×12)

= Rs. 1000

BG = BD - TD

⇒ BD = BG + TD

= 360 + 1000

= Rs. 1360

QUESTION: 6

The true discount on a certain sum due 6 months hence at 15% is Rs. 240. What is the banker's discount on the same sum for the same time at the same rate?

Solution:

Given in the question,

True Discount = 240

Rate of interest = 15%

Time = 6 months = 1/2 year

As we know the formula ,

True Discount = Banker's Gain × 100

Time in years x Rate of Interest

⇒ 240 = Banker's Gain × 100/(1/2 × 15)

⇒ 240 = Banker's Gain × (100 x 2)/(1 × 15)

⇒ 24 = Banker's Gain × (10 x 2)/(1 × 15)

⇒ 24 = Banker's Gain × (2 x 2)/(1 × 3 )

⇒ 6 = Banker's Gain × 1/3

⇒ Banker's Gain = Rs. 6 x 3

⇒ Banker's Gain = Rs. 18

Apply the formula, As we know that ,

Banker's Gain = Banker's Discount − True Discount

⇒ 18 = Banker's Discount − 240

⇒ Banker's Discount = Rs. 258

QUESTION: 7

A bill is discounted at 10% per annum. If banker's discount is allowed, at what rate percent should the proceeds be invested so that nothing will be lost?

Solution:

Let the amount = Rs. 100

Then BD = Rs.10 (∵ banker's discount, BD is the simple Interest on the face value of the bill for unexpired time and bill is discounted at 10% per annum)

Proceeds = Rs. 100 - Rs. 10 = Rs. 90

Hence we should get Rs. 10 as the interest of Rs. 90 for 1 year so that nothing will be lost

⇒ 10 = (90×1×R)/100

⇒ R = (10×100)/90

= 100/9

= 11 1/9%

QUESTION: 8

The banker's discount on a sum of money for 3 years is Rs. 1116. The true discount on the same sum for 4 years is Rs. 1200. What is the rate percent?

Solution:

BD for 3 years = Rs.1116

BD for 4 years = (1116/3)×4

= Rs. 1488

TD for 4 years = Rs.1200

F = (BD×TD)/(BD−TD)

= (1488×1200)/(1488−1200)

= (1488×1200)/288

= (124×1200)/24

= (124×100)/2

= 62×100

= Rs.6200

⇒ Rs. 1488 is the simple interest on Rs. 6200 for 4 years

⇒1488 = (6200×4×R)/100

⇒ R = (1488×100)/(6200×4)

= (372×100)/(6200)

= 372/62

= 6%

QUESTION: 9

The true discount on a bill of Rs. 2160 is Rs. 360. What is the banker's discount?

Solution:

F = Rs. 2160

TD = Rs. 360

PW = F - TD = 2160 - 360 = Rs. 1800

True Discount is the Simple Interest on the present value for unexpired time

⇒ Simple Interest on Rs. 1800 for unexpired time = Rs. 360

Banker's Discount is the Simple Interest on the face value of the bill for unexpired time

= Simple Interest on Rs. 2160 for unexpired time

= (360/1800)×2160

= 1/5×2160

= Rs.432

QUESTION: 10

A banker paid Rs.5767.20 for a bill of Rs.5840, drawn of Apr 4 at 6 months. If the rate of interest was 7%, what was the day on which the bill was discounted?

Solution:

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