Compound vs Simple Interest — If the compound interest on a sum for 2 years at 12.5% p.a. is Rs. 170, what is the simple interest for 2 years at the same rate?

Introduction / Context:
From the given compound interest amount and rate, we can back out the principal. Then we compute the two-year simple interest at the same rate.

Given Data / Assumptions:

• r = 12.5% = 0.125 per annum.
• Time = 2 years.
• CI (2 years) = Rs. 170.

Concept / Approach:
For 2 years: CI = P[(1 + r)^2 − 1]. Solve for P, then SI_2y = P * r * 2.

Step-by-Step Solution:
(1 + 0.125)^2 − 1 = 1.265625 − 1 = 0.265625.P = 170 / 0.265625 = 640.SI (2 years) = 640 * 0.125 * 2 = Rs. 160.

Verification / Alternative check:
Check CI: 640 * 0.265625 = 170 (given).

Why Other Options Are Wrong:
152.50, 162.50, 150, 155 do not equal P*r*2 for P = 640.

Common Pitfalls:
Arithmetic slip when squaring 1.125 or converting 12.5% into decimal.

Final Answer:
Rs. 160