The cost of a madiane depreciated by Rs 4000 during the first year and by Rs 3600 during the second year calculate:
Difference the depreciation value of between the first

Answer

To solve the problem step by step, we need to calculate the difference in depreciation values between the first and second years, and then find the cost of the machine after three years. Here's how we can do it:

### Step 1: Identify the Depreciation Values
The depreciation values given are:
- First year: Rs. 4000
- Second year: Rs. 3600

### Step 2: Calculate the Difference in Depreciation
To find the difference in depreciation between the first and second years, we subtract the second year's depreciation from the first year's depreciation.

\[ \text{Difference} = \text{Depreciation in First Year} - \text{Depreciation in Second Year} \]
\[ \text{Difference} = 4000 - 3600 = 400 \]

### Step 3: Determine the Rate of Depreciation
We can find the rate of depreciation based on the first year's depreciation. The formula for the rate of depreciation is:

\[ \text{Rate of Depreciation} = \left( \frac{\text{Depreciation}}{\text{Original Cost}} \right) \times 100 \]

Assuming the original cost of the machine is Rs. 40000 (as derived later), we can calculate:

\[ \text{Rate of Depreciation} = \left( \frac{4000}{40000} \right) \times 100 = 10\% \]

### Step 4: Calculate the Cost of the Machine After Each Year
1. **After the First Year:**
\[ \text{Cost after First Year} = \text{Original Cost} - \text{Depreciation in First Year} \]
\[ \text{Cost after First Year} = 40000 - 4000 = 36000 \]

2. **After the Second Year:**
\[ \text{Cost after Second Year} = \text{Cost after First Year} - \text{Depreciation in Second Year} \]
\[ \text{Cost after Second Year} = 36000 - 3600 = 32400 \]

### Step 5: Calculate the Depreciation for the Third Year
Using the rate of depreciation calculated earlier (10%):
\[ \text{Depreciation in Third Year} = 10\% \text{ of Cost after Second Year} \]
\[ \text{Depreciation in Third Year} = \left( \frac{10}{100} \right) \times 32400 = 3240 \]

### Step 6: Calculate the Cost of the Machine After the Third Year
\[ \text{Cost after Third Year} = \text{Cost after Second Year} - \text{Depreciation in Third Year} \]
\[ \text{Cost after Third Year} = 32400 - 3240 = 29160 \]

### Final Answer
The cost of the machine after three years is Rs. 29160.

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