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

Answer

To calculate the rate of depreciation based on the given information, we can follow these steps:

### Step 1: Identify the depreciation values
We are given the depreciation values for the second and third years:
- Depreciation in the second year = ₹4,752
- Depreciation in the third year = ₹4,181.76

### Step 2: Calculate the difference in depreciation
To find the difference in depreciation between the second and third years, we subtract the third year's depreciation from the second year's depreciation:
\[ \text{Difference} = 4752 - 4181.76 = 570.24 \]

### Step 3: Set up the formula for depreciation
The difference in depreciation can be expressed in terms of the principal amount (the value at the start of the second year) and the rate of depreciation (R):
\[ \text{Difference} = \text{Principal} \times \frac{R}{100} \]
Where:
- Principal = ₹4,752 (the value at the start of the second year)
- R = rate of depreciation

### Step 4: Substitute the known values into the formula
Now we can substitute the known values into the formula:
\[ 570.24 = 4752 \times \frac{R}{100} \]

### Step 5: Solve for R
To isolate R, we first multiply both sides of the equation by 100:
\[ 57024 = 4752 \times R \]
Next, divide both sides by 4752:
\[ R = \frac{57024}{4752} \]
Calculating this gives:
\[ R = 12 \]

### Step 6: State the rate of depreciation
Thus, the rate of depreciation is:
\[ \text{Rate of depreciation} = 12\% \]

### Final Answer:
The rate of depreciation is 12%.

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