Simple Interest — Two-part split with equal interests: Rs 2600 is split into two parts so that interest on one part at 10% for 5 years equals the interest on the other part at 9% for 6 years. What is the amount invested at 10%?

Introduction / Context:
When two sums earn equal simple interest over different time–rate combinations, the equality condition directly relates the two principals. With the total known, we can solve for each part.

Given Data / Assumptions:

• Total = Rs 2600
• Part X at 10% for 5 years
• Part (2600 − X) at 9% for 6 years
• Interests are equal

Concept / Approach:
Set X * 0.10 * 5 = (2600 − X) * 0.09 * 6 and solve for X. This is a linear equation in X.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 1150, 1200, 1250, 1450 do not satisfy the equal-interest constraint with the given total and rates.

Common Pitfalls:

• Mistaking 9% for 0.9 in decimal; correct is 0.09.
• Forgetting total is fixed at 2600.

Final Answer:
Rs. 1350.