Recover the amount due from a given true discount: If the true discount on a sum due 2 years hence at 7% per annum (simple) is ₹ 672, find the sum due (future amount).
Aptitude
True Discount
Difficulty: Easy
Choose an option
-
A₹ 5500
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B₹ 5425
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C₹ 5472
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D₹ 5300
Answer
Correct Answer: ₹ 5472
Explanation
Introduction / Context:Given true discount TD, time t, and rate r, the due amount A can be found by inverting TD = A * (r * t) / (1 + r * t). This is a standard reverse-calculation task in true discount problems.
Given Data / Assumptions:
- TD = 672.
- t = 2 years.
- r = 7% p.a. simple ⇒ r * t = 0.14.
Concept / Approach:TD = A * 0.14 / 1.14 ⇒ TD = A * (7/50) / (57/50) = A * (7/57). Therefore A = TD * (57/7).
Step-by-Step Solution:A = 672 * 57 / 7 = 96 * 57 = 5472.
Verification / Alternative check:Compute PW = A − TD = 5472 − 672 = 4800. Interest on PW for 2 years at 7% = 4800 * 0.07 * 2 = 672 = TD, confirming correctness.
Why Other Options Are Wrong:
- 5500, 5425, 5300 are not equal to 672 * 57 / 7 and will not produce TD = 672 with the given r and t.
Common Pitfalls:
- Mistaking TD as A * r * t (banker’s discount), which would give A = 672 / 0.14 = 4800 (that is actually the present worth, not the future amount).
Final Answer:₹ 5472