Find the sum from SI and TD: The simple interest (SI) and the true discount (TD) on a certain future sum for a given time and rate are Rs. 25 and Rs. 20 respectively. What is the face value (sum due)?

Introduction / Context: For a future sum S due after a time t at rate r, the true discount (TD) relates to simple interest (SI) through standard formulas. A useful identity is S = (SI * TD) / (SI − TD) when both SI and TD refer to the same future sum S, same rate, and same time.

Given Data / Assumptions:

• SI = Rs. 25 (on the due sum for the given t and r).
• TD = Rs. 20 (on the same due sum for the same t and r).

Concept / Approach: Using the known relationship S = (SI * TD) / (SI − TD), substitute SI = 25 and TD = 20 to compute S directly without solving for r or t explicitly.

Step-by-Step Solution:

Verification / Alternative check: From TD = S * r * t / (1 + r * t) and SI = S * r * t, the above identity is derived by algebraic elimination of r * t, ensuring consistency.

Why Other Options Are Wrong: Rs. 250, Rs. 200, and Rs. 500 correspond to misapplications of the formula; Rs. 400 is also inconsistent.

Common Pitfalls: Using SI − TD or SI + TD as the sum, or confusing present worth with the face value.

Final Answer: Rs. 100