A manufacturer estimates that his machine depreciates by 15% of its value at the beginning of the year. Find the orginal value (cost of the machine, if it depreciates by रु 5,355 during the second year.

Explanation

To find the original value (cost) of the machine that depreciates by ₹5,355 during the second year, we can follow these steps:

### Step 1: Understand the depreciation process
The machine depreciates by 15% of its value at the beginning of each year. This means that at the end of the first year, the value of the machine will be 85% of its original value (100% - 15% = 85%).

### Step 2: Set up the equations
Let the original value of the machine be \( P \). After the first year, the value of the machine will be:
\[ \text{Value after Year 1} = P \times \left(1 - \frac{15}{100}\right) = P \times 0.85 \]

### Step 3: Calculate the value at the beginning of the second year
At the beginning of the second year, the value of the machine is \( P \times 0.85 \).

### Step 4: Calculate the depreciation during the second year
The depreciation during the second year is 15% of the value at the beginning of the second year:
\[ \text{Depreciation in Year 2} = \left(P \times 0.85\right) \times \frac{15}{100} = P \times 0.85 \times 0.15 \]

We know that this depreciation amount is ₹5,355:
\[ P \times 0.85 \times 0.15 = 5,355 \]

### Step 5: Solve for \( P \)
Rearranging the equation to solve for \( P \):
\[ P = \frac{5,355}{0.85 \times 0.15} \]

Calculating \( 0.85 \times 0.15 \):
\[ 0.85 \times 0.15 = 0.1275 \]

Now substituting back into the equation:
\[ P = \frac{5,355}{0.1275} \]

Calculating \( P \):
\[ P = 42,000 \]

### Final Answer
The original value (cost) of the machine is ₹42,000.

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