Compute true discount from present worth: What is the true discount if the present worth (PW) is ₹ 600 for a period of 4 years at 4% per annum simple interest? (Find the difference between the amount due and PW.)

Introduction / Context: True discount (TD) is the reduction from a future amount due to obtain its present worth under simple interest. If the present worth is known, multiply by (1 + r t) to get the future amount, then subtract PW to get TD.

Given Data / Assumptions:

• PW = ₹ 600.
• r = 4% per annum; t = 4 years.

Concept / Approach: Amount due S = PW * (1 + r t). True discount TD = S − PW. Plug r and t into the formula to compute S and then TD.

Step-by-Step Solution:

Verification / Alternative check: Using TD formula TD = S * r t / (1 + r t): TD = 696 * 0.16 / 1.16 = 96 confirms the same result.

Why Other Options Are Wrong: ₹ 100, ₹ 86, ₹ 84, and ₹ 32 do not match the exact computation for the given PW, rate, and time.

Common Pitfalls: Applying the rate directly to PW as if TD = PW * r t (that gives SI on PW, not TD); forgetting to reconstruct S first.

Final Answer: ₹ 96