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The true discount on Rs 1760 due after a certain time at 12% per annum is Rs 160. The time after which it is due is:
- a)6 months
- b)8 months
- c)9 months
- d)10 months
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The true discount on Rs 1760 due after a certain time at 12% per annum...
P.W. = Rs (1760 – 160) = Rs 1600
∴ S.I. on Rs 1600 at 12% is Rs 160
∴ Time = (100 × 160)/ (1600 × 12) = 5/6
years = (5/6 × 12 months) = 10 months
∴ S.I. on Rs 1600 at 12% is Rs 160
∴ Time = (100 × 160)/ (1600 × 12) = 5/6
years = (5/6 × 12 months) = 10 months
Most Upvoted Answer
The true discount on Rs 1760 due after a certain time at 12% per annum...
Given data:
- Principal amount (P) = Rs 1760
- True discount (D) = Rs 160
- Rate of interest (R) = 12% per annum
Formula for calculating True Discount:
True Discount (D) = P * R * T / 100
Calculation:
- Substituting the given values into the formula:
160 = 1760 * 12 * T / 100
- Solving for T:
T = 16000 / (1760 * 12)
T = 16000 / 21120
T = 0.76 years
Converting years to months:
0.76 years = 0.76 * 12 months
T = 9.12 months
Conclusion:
The time after which the amount is due is approximately 9 months. Since we cannot have a fraction of a month, we will consider the next whole month, which is 10 months. Therefore, the correct answer is option 'D' - 10 months.
- Principal amount (P) = Rs 1760
- True discount (D) = Rs 160
- Rate of interest (R) = 12% per annum
Formula for calculating True Discount:
True Discount (D) = P * R * T / 100
Calculation:
- Substituting the given values into the formula:
160 = 1760 * 12 * T / 100
- Solving for T:
T = 16000 / (1760 * 12)
T = 16000 / 21120
T = 0.76 years
Converting years to months:
0.76 years = 0.76 * 12 months
T = 9.12 months
Conclusion:
The time after which the amount is due is approximately 9 months. Since we cannot have a fraction of a month, we will consider the next whole month, which is 10 months. Therefore, the correct answer is option 'D' - 10 months.
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