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

Introduction / Context:
This question explores how to back calculate the principal when the final amount, rate of simple interest, and time period are known. Instead of being asked for interest directly, we are given the total amount at the end of the period. This type of reverse calculation is common in banking aptitude questions and helps build fluency with simple interest relationships.

Given Data / Assumptions:
Final amount A after 6 years is Rs. 942.
Rate of simple interest r is 9.5 percent per annum.
Time period t is 6 years.
Principal P is unknown and to be determined.
Interest is simple interest with a constant rate over the 6 years.

Concept / Approach:
For simple interest, interest I is given by I = P * r * t / 100. The amount A at the end is A = P + I. Combining these, A = P + P * r * t / 100 = P * (1 + r * t / 100). Since A, r, and t are known, we can solve for P by dividing the amount by the factor (1 + r * t / 100). This factor represents how many times the principal grows in the given time under simple interest.

Step-by-Step Solution:
Write the amount formula under simple interest: A = P * (1 + r * t / 100).Substitute A = 942, r = 9.5, and t = 6.Compute r * t / 100 = 9.5 * 6 / 100.First 9.5 * 6 = 57, so r * t / 100 = 57 / 100 = 0.57.Thus A = P * (1 + 0.57) = P * 1.57.So 942 = P * 1.57.Solve for P: P = 942 / 1.57 = 600 rupees.Therefore, the initial principal invested was Rs. 600.

Verification / Alternative check:
Check simple interest on Rs. 600 at 9.5 percent for 6 years. Interest I is 600 * 9.5 * 6 / 100. Compute 9.5 * 6 = 57, so I = 600 * 57 / 100 = 600 * 0.57 = 342 rupees. Amount A is 600 + 342 = 942 rupees, which matches the given final amount. This confirms that the principal is correctly found.

Why Other Options Are Wrong:
Rs. 616, Rs. 626, and Rs. 636 would each lead to different interest amounts and final totals that do not equal 942 when calculated using the same rate and time.
For example, with Rs. 650 as principal, the amount would be greater than 942, violating the given data.
Only Rs. 600 leads to a final amount of exactly 942 under the specified simple interest conditions.

Common Pitfalls:
Some learners mistakenly treat 9.5 percent as 0.95 instead of 9.5 in the formula, which changes the result drastically. Others may incorrectly subtract interest instead of dividing by the growth factor. Another issue is working with decimals imprecisely when dividing by 1.57. Carefully writing the formula and performing decimal arithmetic step by step helps ensure the correct answer is obtained.

Final Answer:
The initial principal that grows to Rs. 942 in 6 years at 9.5 percent simple interest per annum is Rs. 600.