If an amount becomes Rs. 19965 at a compound interest rate of 10% per annum in 3 years, what was the original principal amount in rupees?

Introduction / Context:
This question checks understanding of how to find the principal when the final amount under compound interest is known. Instead of directly computing the amount from the principal, the learner must reverse the process by effectively dividing the final amount by the growth factor. This is a very common type of compound interest problem in aptitude tests, especially when the rate and time period are neat values like 10% and 3 years.

Given Data / Assumptions:

• Final amount A after 3 years = Rs. 19965.
• Rate of compound interest r = 10% per annum.
• Time period n = 3 years.
• Interest is compounded annually.
• We need to find the principal P such that A = P * (1 + r) ^ n.

Concept / Approach:
With annual compounding, the standard compound interest amount formula is A = P * (1 + r) ^ n, where r is the rate expressed in decimal form. Here r = 10% = 0.10 and n = 3. To find P, we rearrange the formula to P = A / ((1 + r) ^ n). After computing the growth factor (1.10) ^ 3, we divide the known amount 19965 by this factor to recover the original principal. Finally, we match this principal with the most appropriate option from the list provided.

Step-by-Step Solution:
Step 1: Convert rate to decimal form: r = 10% = 0.10. Step 2: Compute the growth factor for 3 years with annual compounding: (1 + r) ^ n = (1.10) ^ 3. Step 3: Calculate (1.10) ^ 2 = 1.21 and then multiply once more by 1.10, giving (1.10) ^ 3 = 1.331. Step 4: Use the rearranged formula P = A / ((1 + r) ^ n) = 19965 / 1.331. Step 5: Perform the division: 19965 / 1.331 = 15000. Step 6: Therefore, the principal amount P that grows to 19965 in three years at 10% compound interest is Rs. 15000.

Verification / Alternative check:
We can verify by moving forward from the principal. If P = 15000, then A = 15000 * (1.10) ^ 3. First year amount is 15000 * 1.10 = 16500. Second year amount is 16500 * 1.10 = 18150. Third year amount is 18150 * 1.10 = 19965. This matches the given final amount exactly, which confirms that the principal we computed is correct. The neat integer result also fits well with typical competitive exam design where the correct option is usually a clean rounded figure.

Why Other Options Are Wrong:
16000 is too high for the principal. If we used 16000, the amount after 3 years would be 16000 * 1.331 = 21296, which is larger than 19965. Similarly, 17000 would lead to an amount of 17000 * 1.331 = 22627, and 18000 would give 18000 * 1.331 = 23958, both far above the target amount. The option 14000 is too small, since 14000 * 1.331 = 18634, which is less than 19965. Therefore, only 15000 produces the exact required amount under the given conditions.

Common Pitfalls:
Students sometimes confuse simple interest and compound interest and try to use the simple interest formula to reverse the calculation. Others miscalculate the power (1.10) ^ 3, for example by adding three times 0.10 instead of multiplying three times by 1.10. Another frequent mistake is to divide by the simple interest percent value rather than by the full growth factor. Careless rounding during intermediate steps can also give a principal value that does not match any option precisely. It is better to carry out the exact multiplication and division with 1.331 to obtain the correct result.

Final Answer:
The original principal that would amount to Rs. 19965 in 3 years at 10% per annum compounded annually is Rs. 15000, which corresponds to option B.