Final answer:
The difference in rates is calculated by dividing the difference in simple interest by the product of the principal amount and time. For a difference of Rs.18 over Rs.1,500 for 3 years, the rate difference is 0.004 or 0.4%, which is option (a).
Step-by-step explanation:
The student asked what the difference in their rates is, given that the difference in simple interest of a sum of Rs.1,500 invested for 3 years is Rs.18. To solve this, we need to understand how simple interest is calculated. The formula for simple interest is I = PRT, where I is the interest, P is the principal amount, R is the rate, and T is the time in years. In the given problem, we can create an equation based on the difference in interest due to a difference in rates for the same principal and time.
Let R1 be the first rate and R2 the second rate, with a difference of R2 - R1. The difference in simple interest can similarly be represented as I2 - I1 = P * (R2 - R1) * T. Plugging in the given values:
18 = 1500 * (R2 - R1) * 3
18 = 4500 * (R2 - R1)
(R2 - R1) = 18 / 4500
(R2 - R1) = 0.004
The difference in their rates is 0.004, which is equal to 0.4% when converted to a percentage. Hence, the correct answer to the student's question is option (a) 0.4.