During every financial year, the value of a machine depreciates by 12%. Find the original cost of a machine which depreciates by रु 2,640 during the second financial year of its purchase.

Explanation

To find the original cost of the machine that depreciates by ₹2,640 during the second financial year, we can follow these steps:

### Step 1: Understand the Depreciation
The machine depreciates by 12% every year. This means that at the end of each financial year, the value of the machine is reduced by 12% of its value at the beginning of that year.

### Step 2: Set Up the Initial Value
Let the original cost of the machine be \( P \).

### Step 3: Calculate the Value After the First Year
At the end of the first year, the value of the machine after depreciation can be calculated as follows:
\[ \text{Value after 1st year} = P - (12\% \text{ of } P) = P - 0.12P = 0.88P \]

### Step 4: Calculate the Depreciation for the Second Year
At the beginning of the second year, the value of the machine is \( 0.88P \). The depreciation for the second year is:
\[ \text{Depreciation during 2nd year} = 12\% \text{ of } 0.88P = 0.12 \times 0.88P = 0.1056P \]

### Step 5: Set Up the Equation
According to the problem, the depreciation during the second financial year is given as ₹2,640. Therefore, we can set up the equation:
\[ 0.1056P = 2640 \]

### Step 6: Solve for \( P \)
To find \( P \), we can rearrange the equation:
\[ P = \frac{2640}{0.1056} \]

Calculating this gives:
\[ P = 25,000 \]

### Conclusion
The original cost of the machine is ₹25,000.

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