The compound interest on a certain sum of money for 2 years is Rs 832 and the simple interest on the same sum for the same period is Rs 800. What is the difference between the compound interest and simple interest on the same sum for 3 years?

Introduction:
This problem requires you to work with both simple and compound interest for the same principal and rate, using given information for 2 years to determine the rate and principal, and then extending the calculation to 3 years to find the new difference between compound interest and simple interest.

Given Data / Assumptions:

• Simple interest (SI) for 2 years = Rs 800.
• Compound interest (CI) for 2 years = Rs 832.
• Same principal P and rate r for both types of interest.
• Interest is compounded annually.
• We need the difference between CI and SI for 3 years.

Concept / Approach:
First use the simple interest formula SI = P * r * t / 100 to form one equation. Then use the compound interest formula for 2 years to form another equation. Solve the system to find P and r. Then compute SI and CI for 3 years and find the new difference CI − SI.

Step-by-Step Solution:
For 2 years, SI2 = P * r * 2 / 100 = 800, so P * r / 100 = 400.CI2 = P * (1 + r/100)^2 − P = 832.Let x = r/100. Then CI2 = P * [(1 + x)^2 − 1] = P * (2x + x^2) = 832.But P * x = 400, so 2P * x = 800.Thus 800 + P * x^2 = 832, so P * x^2 = 32.Divide P * x^2 = 32 by P * x = 400 to find x:x^2 / x = 32 / 400, so x = 0.08, hence r = 8%.P * x = 400 means P * 0.08 = 400, so P = 5000.Now for 3 years: SI3 = P * r * 3 / 100 = 5000 * 8 * 3 / 100 = Rs 1200.CI3 = P * (1 + 0.08)^3 − P = 5000 * (1.08)^3 − 5000.(1.08)^3 ≈ 1.259712, so CI3 ≈ 5000 * 1.259712 − 5000 = 6298.56 − 5000 = Rs 1298.56.Difference for 3 years: CI3 − SI3 = 1298.56 − 1200 = Rs 98.56.

Verification / Alternative Check:
You can also compute year wise interest. After finding P and r, calculate the interest added each year under compound interest and sum over 3 years, then compare with SI over 3 years. This gives the same difference of Rs 98.56.

Why Other Options Are Wrong:
Rs 48 and Rs 66.56: These are too small and do not match the computed difference for 3 years.Rs 88.56: Close but slightly smaller than the correct value; it may come from rounding errors or miscalculations.None of these: Incorrect because Rs 98.56 fits perfectly.

Common Pitfalls:
One common error is to incorrectly assume that the difference for 3 years is simply 1.5 times the difference for 2 years, which is not true for compound interest. Others may apply the shortcut formula for difference incorrectly or forget to solve for both P and r before extending the time period.

Final Answer:
The difference between compound interest and simple interest on the same sum for 3 years is Rs 98.56.