The present value of an old car is Rs. 5,40,000. Its value depreciates at 25% per annum What was its value (in Rs) 2 years ago?

Options

A. 9,60,000
B. 7,20,000
C. 6,30,000
D. 2,16,000

Answer

To find the value of the car two years ago given its present value and the rate of depreciation, we can follow these steps:

### Step 1: Understand the Depreciation Rate
The car depreciates at a rate of 25% per annum. This means that each year, the value of the car is 75% of its value from the previous year (100% - 25% = 75%).

### Step 2: Convert the Depreciation Rate to a Fraction
The depreciation rate of 25% can be expressed as a fraction:
- 25% = 25/100 = 1/4
- Therefore, the remaining value after depreciation is 3/4.

### Step 3: Calculate the Value of the Car Two Years Ago
Let the value of the car two years ago be \( V \).
After one year, the value of the car would be:
\[ V \times \frac{3}{4} \]
After two years, the value of the car would be:
\[ V \times \left(\frac{3}{4}\right)^2 \]
This can be simplified to:
\[ V \times \frac{9}{16} \]

### Step 4: Set Up the Equation
We know the present value of the car is Rs. 5,40,000. Therefore, we can set up the equation:
\[ V \times \frac{9}{16} = 5,40,000 \]

### Step 5: Solve for \( V \)
To find \( V \), we can rearrange the equation:
\[ V = 5,40,000 \times \frac{16}{9} \]
Now, calculate \( V \):
\[ V = 5,40,000 \times \frac{16}{9} = 5,40,000 \times 1.7777... \]
\[ V = 9,60,000 \]

### Conclusion
The value of the car two years ago was Rs. 9,60,000.

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