A sum of ₹15,200 is divided into two parts. For 1 year at simple interest: The simple interest on the first part at 25% per annum equals the simple interest on the second part at 13% per annum. What is the simple interest (in rupees) earned on each part for 1 year?

Introduction:
This problem tests splitting a total principal into two parts such that the simple interest earned on each part (for the same time) becomes equal even though the rates differ. Because the time is the same (1 year), equal interest implies the principals are inversely proportional to the rates. We use a variable split, set the two simple interests equal, solve for the parts, and then compute the interest value.

Given Data / Assumptions:

• Total sum = ₹15,200
• First part earns SI at 25% per annum for 1 year
• Second part earns SI at 13% per annum for 1 year
• Interests are equal for the same time
• Formula: SI = (P * r * t) / 100 with t = 1

Concept / Approach:
Let first part be x and second part be (15200 - x). Since t is 1 year, SI1 = 0.25x and SI2 = 0.13(15200 - x). Set SI1 = SI2 and solve for x. Then compute SI for either part for 1 year (they will match by construction).

Step-by-Step Solution:
Let first principal = x, second principal = 15200 - x SI1 for 1 year at 25%: SI1 = (x * 25 * 1) / 100 = 0.25x SI2 for 1 year at 13%: SI2 = ((15200 - x) * 13 * 1) / 100 = 0.13(15200 - x) Given SI1 = SI2: 0.25x = 0.13(15200 - x) 0.25x = 1976 - 0.13x 0.38x = 1976 x = 1976 / 0.38 = 5200 Then second part = 15200 - 5200 = 10000 Interest on each part: SI1 = 0.25 * 5200 = 1300 (and SI2 = 0.13 * 10000 = 1300)

Verification / Alternative check:
Compute both interests directly: 25% of 5200 for 1 year = 1300, and 13% of 10000 for 1 year = 1300. Equal as required, confirming correctness.

Why Other Options Are Wrong:
₹2,500 and ₹3,250 are too high for one-year interest under these splits. ₹1,625 and ₹1,520 come from incorrect splitting or wrong equality setup. Only ₹1,300 satisfies both rates with the correct split.

Common Pitfalls:
Forgetting that time is 1 year (so SI is directly rate percent of principal), setting up equality on amounts instead of interest, or swapping the rates for the two parts.

Final Answer:
The simple interest on each part for 1 year is ₹1,300.