Find rate percent from true discount: The true discount on Rs. 340 due 5 years hence is Rs. 40. What is the simple-interest rate per annum?

Introduction / Context:
True discount (TD) relates the future sum S, rate r, and time t under simple interest via TD = S * r * t / (1 + r * t). With S, TD, and t known, solve for r. This applies to bills due at a future date where TD is the deduction to obtain present worth.

Given Data / Assumptions:

• S = Rs. 340 (amount due after 5 years).
• TD = Rs. 40.
• t = 5 years.

Concept / Approach:
Let u = r * t. Then TD = S * u / (1 + u). Solve u from 40 = 340 * u / (1 + u), then obtain r = u / t. Convert the decimal to a mixed fraction percentage for clarity.

Step-by-Step Solution:

Verification / Alternative check:
Substitute r = 2 2/3% back: u = r t = 2/75 * 5 = 2/15; TD = 340 * (2/15) / (1 + 2/15) = 340 * (2/15) / (17/15) = 340 * (2/17) = 40.

Why Other Options Are Wrong:
3%, 3 1/3%, and 3 2/3% are higher than required; 2% is lower. Only 2 2/3% satisfies the equation exactly.

Common Pitfalls:
Dropping the (1 + r t) term; treating TD as S r t, which would give an inflated rate.

Final Answer:
2 2/3%