An investor places his savings in the stock market. The value of his investment increases by 12% in the first year and by 9% in the second year. After these two years, the value of his investments becomes Rs 97,664. How much did he originally invest (in Rs)?

Introduction / Context:
This problem deals with successive percentage increases over two years. It models real life situations where investments grow year by year at different rates. The task is to work backwards from the final amount to find the initial investment. The key idea is to understand compound growth through multiplication by growth factors.

Given Data / Assumptions:

• Initial investment is P (unknown).
• Increase in first year = 12% of the amount at the beginning of the year.
• Increase in second year = 9% of the amount at the beginning of the second year.
• Final value after two years = Rs 97,664.

Concept / Approach:
A 12% increase means the amount is multiplied by 1.12. A 9% increase means multiplication by 1.09. After two years, the total multiplication factor is 1.12 * 1.09. The final amount equals the initial investment times this combined factor. Thus, we write 97664 = P * 1.12 * 1.09 and solve for P by dividing the final value by the product of the growth factors.

Step-by-Step Solution:
Step 1: Let the initial investment be P. Step 2: After the first year, amount = P * 1.12. Step 3: After the second year, new amount = (P * 1.12) * 1.09 = P * 1.12 * 1.09. Step 4: Given that this final amount is Rs 97,664. Step 5: So P * 1.12 * 1.09 = 97664. Step 6: Compute the combined factor: 1.12 * 1.09 = 1.2208. Step 7: Therefore P = 97664 / 1.2208. Step 8: Calculate P = 80000. Step 9: So the initial investment was Rs 80,000.

Verification / Alternative check:
Starting from P = 80000, after first year amount = 80000 * 1.12 = 89600. After second year amount = 89600 * 1.09 = 97664. This matches the given final amount exactly, confirming our solution.

Why Other Options Are Wrong:

• 81000 and 75000: These values, when increased by 12% and then 9%, result in final amounts different from 97664.
• 72000: This is even smaller and would produce a much lower final value.
• 90000: Starting with 90000 would end up with a final amount larger than 97664.

Common Pitfalls:
One frequent mistake is to simply add the percentages and consider the total increase as 21% over two years. That assumes simple rather than compound growth and gives a wrong initial value. Another error is to divide 97664 by only one of the factors instead of the product. Always remember that successive percentage increases multiply, and the correct way to reverse them is to divide by the combined multiplier.

Final Answer:
The investor originally invested Rs 80,000 in the stock market.