The cost of a machine depreciated by rupees 4,752 during the second year and by 4,181.76 during the third year. Calculate :
the original cost of the machine,

Answer

To find the original cost of the machine based on the depreciation values given for the second and third years, we can follow these steps:

### Step 1: Calculate the difference in depreciation
The depreciation during the second year is ₹4,752, and during the third year, it is ₹4,181.76.

To find the difference in depreciation:
\[ \text{Difference} = \text{Depreciation in 2nd year} - \text{Depreciation in 3rd year} \]
\[ \text{Difference} = 4752 - 4181.76 = 570.24 \]

### Step 2: Calculate the rate of depreciation
The difference in depreciation (₹570.24) represents the depreciation amount for one year. We can calculate the rate of depreciation using the depreciation amount from the second year (₹4,752).

The formula for the rate of depreciation is:
\[ \text{Rate of Depreciation} = \left( \frac{\text{Difference}}{\text{Depreciation in 2nd year}} \right) \times 100 \]
\[ \text{Rate of Depreciation} = \left( \frac{570.24}{4752} \right) \times 100 \approx 12\% \]

### Step 3: Set up the original cost
Let’s assume the original cost of the machine is ₹100.

### Step 4: Calculate the cost after the first year
The depreciation for the first year would be:
\[ \text{Depreciation for 1st year} = 12\% \text{ of } 100 = 12 \]
So, the cost after the first year would be:
\[ \text{Cost after 1st year} = 100 - 12 = 88 \]

### Step 5: Calculate the cost after the second year
Now, we calculate the depreciation for the second year based on the remaining cost:
\[ \text{Depreciation for 2nd year} = 12\% \text{ of } 88 = 10.56 \]
So, the cost after the second year would be:
\[ \text{Cost after 2nd year} = 88 - 10.56 = 77.44 \]

### Step 6: Relate the depreciation to the original cost
We know that the depreciation in the second year is ₹4,752. We can set up a proportion:
\[ \frac{10.56}{100} = \frac{4752}{\text{Original Cost}} \]

### Step 7: Solve for the original cost
Cross-multiplying gives:
\[ 10.56 \times \text{Original Cost} = 475200 \]
\[ \text{Original Cost} = \frac{475200}{10.56} \approx 45000 \]

### Conclusion
The original cost of the machine is ₹45,000.

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