A merchant starts with a certain capital and gains annually at the rate of 30%. At the end of 2 years he is worth Rs. 10,000. What was his original capital at the beginning?

Introduction / Context:
This question is about compound percentage growth, similar to compound interest, where a merchant's capital grows by 30% every year. The final amount after 2 years is given and we are asked to work backward to find the original capital. This kind of problem is common in quantitative aptitude and financial mathematics and reinforces the concept of reversing compound growth.

Given Data / Assumptions:

• Annual growth rate = 30%.
• Time period = 2 years.
• Value after 2 years = Rs. 10,000.
• Let the original capital be C rupees.

Concept / Approach:
When capital grows at a rate r per year, the amount after n years is given by C * (1 + r)^n. Here, r = 0.30 and n = 2. So the final amount A is C * (1.30)^2. We know A = 10000, so we set 10000 = C * (1.30)^2 and solve for C. Since (1.30)^2 = 1.69, we have C = 10000 / 1.69. This is a standard reverse compound interest calculation.

Step-by-Step Solution:
Step 1: Let the original capital be C. Step 2: Annual growth factor = 1 + 30% = 1.30. Step 3: After 2 years, amount A = C * (1.30)^2. Step 4: Compute (1.30)^2 = 1.30 * 1.30 = 1.69. Step 5: We are told that after 2 years, A = 10000, so 10000 = C * 1.69. Step 6: Solve for C: C = 10000 / 1.69. Step 7: Perform the division: 10000 / 1.69 ≈ 5917.16. Step 8: Rounding to the nearest rupee, the original capital is approximately Rs. 5,917.

Verification / Alternative check:
Verify using C = 5917. If we grow this by 30% for 2 years, the amount should be approximately 10000. After year 1: 5917 * 1.30 ≈ 7692.1. After year 2: 7692.1 * 1.30 ≈ 9999.73, which is effectively 10000 when rounded. This confirms that starting with about 5917 and applying two successive 30% increases leads us to the final value.

Why Other Options Are Wrong:
Values like 4987, 5148, 6254, and 7000 either produce amounts well below or above 10000 when grown by 30% for 2 years. For example, 7000 * 1.69 = 11830, which is far above 10000. Only 5917 multiplied by 1.69 gives a result close to 10000, so it is the only consistent option with the given data and growth rate.

Common Pitfalls:
Some learners mistakenly treat the growth as simple interest, adding 30% of the original capital twice instead of compounding. This would lead to using a factor of 1 + 2 * 0.30 = 1.60 instead of 1.69. Others may attempt to subtract 30% twice when working backward, which is not equivalent to dividing by 1.69. Understanding that each year's increase is applied to the new amount, not the original, is crucial to solving such problems correctly.

Final Answer:
The merchant's original capital was approximately Rs. 5,917.