Difficulty: Medium
Correct Answer: 15
Explanation:
Introduction / Context:With TD, face amount A, and time t, we can solve for r t and hence for the annual rate r. The derivation is algebraic and direct from the definition of true discount.
Given Data / Assumptions:
Concept / Approach:
TD = A * (r t) / (1 + r t) Let x = r t ⇒ TD = A * x / (1 + x)Step-by-Step Solution:
122 = 2562 * x / (1 + x) ⇒ x = 122 / (2562 − 122) = 122 / 2440 = 0.05 r = x / t = 0.05 / (1/3) = 0.15 = 15% per annumVerification / Alternative check:TD recompute: 2562 * 0.05 / 1.05 = ₹122 (exact).
Why Other Options Are Wrong:12%, 13%, 14% yield different TDs when substituted back into the formula for t = 4 months.
Common Pitfalls:Using months without converting to years; always express t in years for simple interest formulas.
Final Answer:15
Discussion & Comments