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The present worth of a certain bill due sometime hence is Rs. 1296 and the true discount is Rs. 72. What is the banker's discount?
- a)Rs. 76
- b)Rs. 72
- c)Rs. 74
- d)Rs. 4
Correct answer is option 'A'. Can you explain this answer?
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The present worth of a certain bill due sometime hence is Rs. 1296 and...
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The present worth of a certain bill due sometime hence is Rs. 1296 and...
Given, Present worth of a bill = Rs. 1296
True discount = Rs. 72
We know that,
True Discount = Face Value - Present Value
Banker's Discount = Face Value - Amount
Let the face value of the bill be Rs. x.
Now, we can write the following equations:
True Discount = Face Value - Present Value
72 = x - 1296
x = 1368
Banker's Discount = Face Value - Amount
Banker's Discount = x - (Present Value - True Discount)
Banker's Discount = x - (1296 - 72)
Banker's Discount = x - 1224
Banker's Discount = 1368 - 1224
Banker's Discount = Rs. 144
Therefore, the Banker's Discount is Rs. 144. However, this is not an option in the given choices. We need to calculate the cash discount to find the correct option.
Cash Discount = True Discount
Cash Discount = Rs. 72
Now, we can calculate the Banker's Discount using the following formula:
Banker's Discount = (Cash Discount * 100) / (100 - Rate * Time)
Let the rate be r and time be t.
We know that,
True Discount = Simple Interest on the face value for the period of the cash discount.
So, we can write:
True Discount = (Face Value * Rate * Time) / 100
72 = (1368 * r * t) / 100
Let's assume the time period to be one year. So, t = 1.
So, we can write:
72 = (1368 * r) / 100
r = 5.2632%
Now, we can substitute the values in the formula to get the Banker's Discount.
Banker's Discount = (Cash Discount * 100) / (100 - Rate * Time)
Banker's Discount = (72 * 100) / (100 - 5.2632 * 1)
Banker's Discount = Rs. 76
Therefore, the correct option is (a) Rs. 76.
True discount = Rs. 72
We know that,
True Discount = Face Value - Present Value
Banker's Discount = Face Value - Amount
Let the face value of the bill be Rs. x.
Now, we can write the following equations:
True Discount = Face Value - Present Value
72 = x - 1296
x = 1368
Banker's Discount = Face Value - Amount
Banker's Discount = x - (Present Value - True Discount)
Banker's Discount = x - (1296 - 72)
Banker's Discount = x - 1224
Banker's Discount = 1368 - 1224
Banker's Discount = Rs. 144
Therefore, the Banker's Discount is Rs. 144. However, this is not an option in the given choices. We need to calculate the cash discount to find the correct option.
Cash Discount = True Discount
Cash Discount = Rs. 72
Now, we can calculate the Banker's Discount using the following formula:
Banker's Discount = (Cash Discount * 100) / (100 - Rate * Time)
Let the rate be r and time be t.
We know that,
True Discount = Simple Interest on the face value for the period of the cash discount.
So, we can write:
True Discount = (Face Value * Rate * Time) / 100
72 = (1368 * r * t) / 100
Let's assume the time period to be one year. So, t = 1.
So, we can write:
72 = (1368 * r) / 100
r = 5.2632%
Now, we can substitute the values in the formula to get the Banker's Discount.
Banker's Discount = (Cash Discount * 100) / (100 - Rate * Time)
Banker's Discount = (72 * 100) / (100 - 5.2632 * 1)
Banker's Discount = Rs. 76
Therefore, the correct option is (a) Rs. 76.
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The present worth of a certain bill due sometime hence is Rs. 1296 and the true discount is Rs. 72. What is the banker's discount?a)Rs. 76b)Rs. 72c)Rs. 74d)Rs. 4Correct answer is option 'A'. Can you explain this answer?
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