True discount and present worth: A sum due in 146 days at 5% simple interest has a present worth of ₹400. What is the sum due at maturity?

Introduction / Context:
When a sum is due in the future, its present worth (today’s value) is less by the true discount under simple interest. The sum due equals present worth plus the simple interest for the remaining time to maturity. Short-date questions commonly use day-count fractions like 146/365 year.

Given Data / Assumptions:

• Present worth PW = ₹400.
• Rate r = 5% per annum (simple).
• Time t = 146/365 = 0.4 year.

Concept / Approach:
Sum due (face value) A = PW * (1 + r * t). Because interest is simple and time is a fraction of a year, multiply PW by 1 plus the percentage for the fraction 0.4.

Step-by-Step Solution:

Verification / Alternative check:
True discount TD = A − PW = 408 − 400 = ₹8 equals simple interest on PW for 0.4 year at 5%, which is 400 * 0.05 * 0.4 = ₹8.

Why Other Options Are Wrong:
₹410, ₹415, ₹450, ₹404 arise from using wrong day fraction or compounding instead of simple interest.

Common Pitfalls:
Mixing up present worth with face value, or using 360-day convention without instruction, which shifts the result slightly.

Final Answer:
₹408