The value of a vehicle at the end of each year becomes 3/5 of its value at the beginning of that year. If the initial value is Rs. 10,000, what will be its value at the end of three years?

Introduction / Context:
This question is about successive depreciation, where an asset loses a fixed fraction of its value every year. The phrase that the value becomes 3/5 of its value at the beginning of the year means that 2/5 has been depreciated. We must apply this depreciation repeatedly over three years. This is a standard application of repeated percentage or fractional change in quantitative aptitude.

Given Data / Assumptions:
- Initial value of the vehicle is Rs. 10,000.
- At the end of each year, the value becomes 3/5 of the value at the beginning of that year.
- We need the value at the end of three years.
- Depreciation is assumed to be applied once per year, on the current value.

Concept / Approach:
If each year the value is multiplied by a fixed factor, here 3/5, then after n years the value is the initial value multiplied by (3/5)^n. This is similar to compound interest, but with a depreciation factor instead of a growth factor. We must calculate the value after three years using this repeated multiplication.

Step-by-Step Solution:
Initial value V0 = Rs. 10,000. At the end of year 1, value V1 = V0 * (3 / 5) = 10,000 * 3 / 5. Compute V1 = 10,000 * 0.6 = Rs. 6000. At the end of year 2, value V2 = V1 * (3 / 5) = 6000 * 3 / 5. Compute V2 = 6000 * 0.6 = Rs. 3600. At the end of year 3, value V3 = V2 * (3 / 5) = 3600 * 3 / 5. Compute V3 = 3600 * 0.6 = Rs. 2160. Therefore, at the end of three years, the vehicle is worth Rs. 2160.

Verification / Alternative check:
We can also compute in one step using powers. Each year multiplies value by 3/5, so after three years the factor is (3 / 5)^3. Compute (3 / 5)^3 = 27 / 125 = 0.216. Multiply this by the initial value: 10,000 * 0.216 = 2160. This matches the step-by-step calculation and confirms the answer.

Why Other Options Are Wrong:
Rs. 6000 and Rs. 3600: These are the values after one and two years respectively, not after three years.
Rs. 415 and Rs. 2560: These values do not correspond to multiplying by (3 / 5)^3; they represent incorrect arithmetic or wrong interpretation of the fraction.

Common Pitfalls:
A common mistake is to treat depreciation as subtracting a fixed amount each year instead of multiplying by a factor. Another error is to misinterpret the statement and think that 3/5 is the amount depreciated rather than the remaining value. Always read carefully whether the fraction or percentage refers to the remaining value or to the amount lost. Using the compound factor approach is the most reliable method for successive depreciation problems.

Final Answer:
The value of the vehicle at the end of three years will be Rs. 2160.