## Banker's Discount

#### Banker's Discount

1. The present worth (PW) of a sum due sometimes hence is Rs. 5760 and the banker’s gain is Rs. 10. What is the true discount?
1. Rs. 480
2. Rs. 420
3. Rs. 120
4. Rs. 240

1. As per given question,
Present worth PW = 5760
Banker gain = 10
True Discount = ?
As we know the formula,
True Discount = √PW × BG

##### Correct Option: D

As per given question,
Present worth PW = 5760
Banker gain = 10
True Discount = ?
As we know the formula,
True Discount = √PW × BG
True Discount = √Present Worth × Banker's gain
True Discount = √5760 × 10 = √57600 = Rs. 240

1. The banker’s discount of a certain sum of money is Rs. 36 and the true discount on the same sum for the same time is Rs. 30. What is the sum due?
1. Rs. 180
2. Rs. 120
3. Rs. 220
4. Rs. 200

1. Here , Banker's Discount = Rs 36 and True Discount = Rs 30
As we know that ,

 ∴ F = Banker's Discount x True Discount Banker's Discount - True Discount

##### Correct Option: A

Here , Banker's Discount = Rs 36 and True Discount = Rs 30
As we know that ,

 ∴ F = Banker's Discount x True Discount Banker's Discount - True Discount
 ∴ F = 36 x 30 36 - 30

 ∴ F = 36 x 30 6

⇒ F = 36 x 5 = Rs.180
Thus , the sum due is Rs.180 .

1. 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:
1. Rs. 21
2. Rs. 17
3. Rs. 18
4. Rs. 34

1. Given that :- True Discount = Rs. 340 and Present worth = Rs. 3400
We know that ,

 Banker’s gain = ( True Discount ) 2 Present worth

##### Correct Option: D

Given that :- True Discount = Rs. 340 and Present worth = Rs. 3400
We know that ,

 Banker’s gain = ( True Discount ) 2 Present worth
 Banker’s gain = ( 340 ) 2 3400
 Banker’s gain = 340 x 340 = Rs. 34 3400

1. The banker’s gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. What is the present worth?
1. Rs. 600
2. Rs. 500
3. Rs. 400
4. Rs. 300

1. Here , Banker's Gain = Rs. 24 , Time = 2 years and Rate = 10%
According to question ,

 True Discount = Banker's Gain × 100 Time x Rate

##### Correct Option: A

Here , Banker's Gain = Rs. 24 , Time = 2 years and Rate = 10%
According to question ,

 True Discount = Banker's Gain × 100 Time x Rate
 True Discount = 24 × 100 = Rs. 120 2 x 10
 True Discount = PW x Time x Rate 100
 120 = PW x 2 x 10 100

⇒ 1200 = Present Worth x 2
 Present Worth = 1200 = Rs. 600 2

Hence , the present worth is Rs. 600 .

1. What is the present worth of a bill of Rs. 1764 due 2 years hence at 5% compound interest is:
1. Rs. 1600
2. Rs. 1200
3. Rs. 1800
4. Rs. 1400

1. As per the given question ,
Amount = Rs. 1764 , Time = 2 years and Rate =
we know that ,

 Amount = PW 1 + R 2 100

##### Correct Option: A

As per the given question ,
Amount = Rs. 1764 , Time = 2 years and Rate =
we know that ,

 Amount = PW 1 + R 2 100

 1764 = PW 1 + 5 2 100

 1764 = PW 1 + 1 2 20

 1764 = PW 21 2 20

 1764 = PW x 441 400
 PW = 1764 x 400 441

∴ Present worth = 4 x 400 = Rs. 1600