Kalyan purchased a Maruti van for Rs. 1,96,000, and the value of the van depreciates at a fixed rate of 14 2/7 percent per annum. What will be the approximate value of the van after two full years of depreciation at this constant rate?

Introduction / Context:
This is a standard percentage depreciation question. It checks whether you understand how to apply a fixed percentage decrease year after year using the idea of successive percentage changes and compound reduction rather than subtracting a flat amount each year.

Given Data / Assumptions:

• Initial cost price of the Maruti van = Rs. 1,96,000.
• Annual depreciation rate = 14 2/7 percent per year.
• Depreciation is applied every year on the reduced value, not on the original cost.
• The number of years of depreciation to be considered is exactly two years.

Concept / Approach:
A depreciation rate of 14 2/7 percent can be converted into an exact fraction. Since 14 2/7 percent equals 100 / 7 percent, this is 1 / 7 of the value each year. If a quantity loses 1 / 7 of its value, it retains 6 / 7 of its value. For successive years, we multiply the original value by (6 / 7) for each year. Thus the final value after n years is initial value * (retained fraction)^n.

Step-by-Step Solution:
Step 1: Convert 14 2/7 percent to a fraction: 14 2/7 = 100 / 7 percent. Step 2: As a fraction of the value, 100 / 7 percent is (100 / 7) / 100 = 1 / 7. Step 3: Depreciation of 1 / 7 means the van retains 1 − 1 / 7 = 6 / 7 of its value each year. Step 4: After two years, value = 1,96,000 * (6 / 7) * (6 / 7) = 1,96,000 * 36 / 49. Step 5: Compute 1,96,000 / 49 = 4,000, then 4,000 * 36 = 1,44,000.

Verification / Alternative check:
You can approximate 14 2/7 percent as about 14.28 percent and use a calculator or mental estimation. A single year reduces the value from 1,96,000 to around 1,68,000. A second similar reduction leads to a figure near 1,44,000. This supports the exact calculation result and shows the answer is reasonable.

Why Other Options Are Wrong:

• Rs. 1,24,000 represents an excessively large reduction over two years compared to 14 2/7 percent annually.
• Rs. 1,32,000 is still lower than the correctly computed amount and does not match the fraction 36 / 49 of the original price.
• Rs. 1,62,000 is too high and would correspond to a much smaller depreciation rate than given in the question.

Common Pitfalls:
Many learners mistakenly subtract 14 2/7 percent of the original amount twice instead of applying the percentage on the reduced value each year. Others convert the mixed fraction incorrectly. Always convert a mixed percentage such as 14 2/7 percent carefully and use the compound multiplier method to avoid errors.

Final Answer:
The value of the van after two years is Rs. 1,44,000.