At a simple interest rate of 9.5% per annum, a sum of money grows to Rs 942 in 6 years. Using the simple interest relationship between principal, rate, time, and amount, find the initial principal amount that was invested so that it becomes Rs 942 after 6 years.

Introduction / Context:
This problem requires working backwards from the final amount to determine the principal under simple interest. The amount after a given time at a stated rate is known, and the principal is unknown. Such reverse simple interest problems are very common in quantitative aptitude, where candidates must be comfortable rearranging the simple interest formulas and performing accurate calculations with decimal interest rates like 9.5% per annum.

Given Data / Assumptions:

• Final amount after 6 years, A = Rs 942.
• Rate of simple interest, R = 9.5% per annum.
• Time period, T = 6 years.
• Principal P is unknown.
• Interest is calculated using simple interest only.

Concept / Approach:
For simple interest, the relationship between amount and principal is:
Amount A = Principal P + Simple interest SI and
SI = (P * R * T) / 100 Combining, we get:
A = P + (P * R * T) / 100 = P * (1 + (R * T) / 100) Here, A, R, and T are known, so we can rearrange this equation to solve for P. The factor multiplying P is computed first, and then P is found by dividing A by that factor.

Step-by-Step Solution:
Given A = Rs 942, R = 9.5% per annum, T = 6 years. Compute the effective multiplier: 1 + (R * T) / 100. R * T = 9.5 * 6 = 57. (R * T) / 100 = 57 / 100 = 0.57. So the amount factor is 1 + 0.57 = 1.57. Thus A = P * 1.57. Given A = 942, so 942 = 1.57P. P = 942 / 1.57. P = 600. Therefore, the initial principal invested is Rs 600.

Verification / Alternative check:
We can verify by computing the simple interest on Rs 600 at 9.5% per annum for 6 years. Simple interest SI = (600 * 9.5 * 6) / 100. First compute 9.5 * 6 = 57, so SI = (600 * 57) / 100 = 34200 / 100 = 342. The final amount is P + SI = 600 + 342 = 942, which matches the given amount. This confirms that P = Rs 600 is correct.

Why Other Options Are Wrong:
If P were Rs 616, multiplying by 1.57 gives approximately 967.12, not 942.
If P were Rs 626, 626 * 1.57 is about 982.82, again not 942.
If P were Rs 636, 636 * 1.57 is greater than 942, and if P were Rs 650, 650 * 1.57 = 1020.5, which is also incorrect. Only Rs 600 gives the exact final amount of Rs 942 when the simple interest is applied.

Common Pitfalls:
Mistakes often occur when multiplying a decimal rate by time or when handling the decimal factor for the amount. Some students forget to convert 9.5% properly or try to use compound interest formulas instead of simple interest. Others may compute A = P + SI but then not factor P correctly. Writing the combined formula for A directly in terms of P and carefully computing the factor 1.57 helps to avoid such errors.

Final Answer:
The initial principal amount that was invested so that it becomes Rs 942 in 6 years is Rs 600.