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The banker's discount on a certain amount due 2 years hence is 11/10 of the true discount. What is the rate percent?
- a)1%
- b)5%
- c)10%
- d)12%
Correct answer is option 'B'. Can you explain this answer?
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The banker's discount on a certain amount due 2 years hence is 11/10 o...
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The banker's discount on a certain amount due 2 years hence is 11/10 o...
Given:
- The banker's discount on a certain amount due 2 years hence is 11/10 of the true discount.
To find:
- The rate percent.
Explanation:
Let's assume the principal amount is P.
Banker's Discount (BD):
- Banker's discount is the difference between the face value of the bill and the amount paid by the banker to the customer in advance.
- The banker's discount is given as 11/10 of the true discount.
- Let's assume the true discount is D.
- So, BD = 11/10 * D
True Discount (TD):
- True discount is the difference between the amount due and the amount paid in advance.
- The amount due is P and it is due 2 years hence.
- Let's assume the rate percent is R.
- So, TD = P * R * 2 / 100
Equating BD to TD:
- BD = TD
- 11/10 * D = P * R * 2 / 100
Cancelling out common factors:
- 11/10 * D = P * R * 2 / 100
- 11 * D = 10 * P * R * 2 / 100
- 11 * D = 2 * P * R / 10
- 11 * D = P * R / 5
Simplifying the equation:
- D = P * R / 55
Conclusion:
- From the equation D = P * R / 55, we can see that the true discount is directly proportional to the principal amount and the rate percent.
- Since the true discount cannot be zero, neither the principal amount nor the rate percent can be zero.
- Therefore, the rate percent (R) must be a non-zero value.
- Among the given options, option B) 5% is the only non-zero value.
- Hence, the correct answer is option B) 5%.
- The banker's discount on a certain amount due 2 years hence is 11/10 of the true discount.
To find:
- The rate percent.
Explanation:
Let's assume the principal amount is P.
Banker's Discount (BD):
- Banker's discount is the difference between the face value of the bill and the amount paid by the banker to the customer in advance.
- The banker's discount is given as 11/10 of the true discount.
- Let's assume the true discount is D.
- So, BD = 11/10 * D
True Discount (TD):
- True discount is the difference between the amount due and the amount paid in advance.
- The amount due is P and it is due 2 years hence.
- Let's assume the rate percent is R.
- So, TD = P * R * 2 / 100
Equating BD to TD:
- BD = TD
- 11/10 * D = P * R * 2 / 100
Cancelling out common factors:
- 11/10 * D = P * R * 2 / 100
- 11 * D = 10 * P * R * 2 / 100
- 11 * D = 2 * P * R / 10
- 11 * D = P * R / 5
Simplifying the equation:
- D = P * R / 55
Conclusion:
- From the equation D = P * R / 55, we can see that the true discount is directly proportional to the principal amount and the rate percent.
- Since the true discount cannot be zero, neither the principal amount nor the rate percent can be zero.
- Therefore, the rate percent (R) must be a non-zero value.
- Among the given options, option B) 5% is the only non-zero value.
- Hence, the correct answer is option B) 5%.
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Community Answer
The banker's discount on a certain amount due 2 years hence is 11/10 o...
T.D = B.D×100/100+(R×T) T.D = 11/10T.D×100/100+(R×2)(100+2R)T.D=110 T.D2R=10R=5%
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The banker's discount on a certain amount due 2 years hence is 11/10 of the true discount. What is the rate percent?a)1%b)5%c)10%d)12%Correct answer is option 'B'. Can you explain this answer?
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