Simple Interest — Three parts with equal interest earnings: Rs 1440 is lent in three parts so that the interest on the first at 2% for 3 years, the second at 3% for 4 years, and the third at 4% for 5 years are equal. What is the difference between the largest and smallest parts?

Introduction / Context:
Equal SI on different parts over different time–rate products implies those parts are inversely proportional to the respective (rate * time) values. With the total known, we apportion by the reciprocal weights and compare extremes.

Given Data / Assumptions:

• Part1: r * t = 0.02 * 3 = 0.06
• Part2: r * t = 0.03 * 4 = 0.12
• Part3: r * t = 0.04 * 5 = 0.20
• Sum of parts = Rs 1440
• All three interests equal

Concept / Approach:
If I1 = I2 = I3, then P1 * 0.06 = P2 * 0.12 = P3 * 0.20 = k. Hence P1 : P2 : P3 = 1/0.06 : 1/0.12 : 1/0.20 = 16.666... : 8.333... : 5 = 50 : 25 : 15 upon scaling.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• Other numeric differences do not match the proportional allocation.

Common Pitfalls:

• Proportioning directly with r or t alone instead of r * t product.

Final Answer:
₹ 560.