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The present worth of a sum due sometimes hence is Rs.5760 and the banker's gain is Rs.10. What is the true discount?
- a) Rs. 480
- b) Rs. 420
- c) Rs. 120
- d) Rs. 240
Correct answer is option `D`. Can you explain this answer?
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Present Worth and Banker's Gain
To find the true discount, we need to understand the concept of present worth and banker's gain.
Present worth refers to the amount of money that is equivalent to a future sum of money at a given interest rate. It is the value of the sum in today's terms.
Banker's gain, on the other hand, is the excess amount that a banker charges when he discounts a bill or a promissory note. It is the difference between the true discount and the present worth.
Given Information
In this question, we are given that the present worth of a sum due is Rs. 5760 and the banker's gain is Rs. 10. We need to find the true discount.
Solution
Let's assume the true discount as 'x'.
The present worth of the sum due is given by the equation:
Present Worth = Sum Due - True Discount
Rs. 5760 = Sum Due - x
We are also given that the banker's gain is Rs. 10.
Banker's Gain = Sum Due - Present Worth
Rs. 10 = Sum Due - Rs. 5760
Simplifying the equation, we get:
Sum Due = Rs. 5770
Substituting this value back into the equation for present worth, we have:
Rs. 5760 = Rs. 5770 - x
Solving for 'x', we find:
x = Rs. 5770 - Rs. 5760
x = Rs. 10
Therefore, the true discount is Rs. 10.
Conclusion
The true discount in this scenario is Rs. 10. This means that the sum due can be discounted by Rs. 10 to obtain the present worth of Rs. 5760.
To find the true discount, we need to understand the concept of present worth and banker's gain.
Present worth refers to the amount of money that is equivalent to a future sum of money at a given interest rate. It is the value of the sum in today's terms.
Banker's gain, on the other hand, is the excess amount that a banker charges when he discounts a bill or a promissory note. It is the difference between the true discount and the present worth.
Given Information
In this question, we are given that the present worth of a sum due is Rs. 5760 and the banker's gain is Rs. 10. We need to find the true discount.
Solution
Let's assume the true discount as 'x'.
The present worth of the sum due is given by the equation:
Present Worth = Sum Due - True Discount
Rs. 5760 = Sum Due - x
We are also given that the banker's gain is Rs. 10.
Banker's Gain = Sum Due - Present Worth
Rs. 10 = Sum Due - Rs. 5760
Simplifying the equation, we get:
Sum Due = Rs. 5770
Substituting this value back into the equation for present worth, we have:
Rs. 5760 = Rs. 5770 - x
Solving for 'x', we find:
x = Rs. 5770 - Rs. 5760
x = Rs. 10
Therefore, the true discount is Rs. 10.
Conclusion
The true discount in this scenario is Rs. 10. This means that the sum due can be discounted by Rs. 10 to obtain the present worth of Rs. 5760.
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The present worth of a sum due sometimes hence is Rs.5760 and the banker's gain is Rs.10. What is the true discount?a) Rs. 480b) Rs. 420c) Rs. 120d) Rs. 240Correct answer is option `D`. Can you explain this answer?
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