The cost of a machine depreciated by रु 4,000 during the first year and by रु 3,600 during the second year. Calculate :
(i) the rate of depreciation.
(ii) the orginal cost of the machine.
(iii) its cost at the end of the third year.

Explanation

Let's solve the problem step by step.

### Step 1: Calculate the rate of depreciation
The depreciation during the first year is ₹4,000, and during the second year, it is ₹3,600.

First, we find the difference in depreciation:
\[ \text{Difference} = \text{Depreciation in Year 1} - \text{Depreciation in Year 2} = 4000 - 3600 = 400 \]

Now, we can find the rate of depreciation based on the first year's depreciation:
\[ \text{Rate of Depreciation} = \left(\frac{\text{Difference}}{\text{Depreciation in Year 1}}\right) \times 100 = \left(\frac{400}{4000}\right) \times 100 = 10\% \]

### Step 2: Calculate the original cost of the machine
Let the original cost of the machine be \( x \).

After the first year, the value of the machine will be:
\[ \text{Value after Year 1} = x - \text{Depreciation in Year 1} = x - 4000 \]

After the second year, the depreciation is 10% of the value after the first year:
\[ \text{Depreciation in Year 2} = 10\% \text{ of } (x - 4000) = 0.10 \times (x - 4000) \]

Given that the depreciation in the second year is ₹3,600, we can set up the equation:
\[ 0.10 \times (x - 4000) = 3600 \]

Solving for \( x \):
\[ x - 4000 = 36000 \quad \text{(Multiplying both sides by 10)} \]
\[ x = 40000 \]

### Step 3: Calculate the cost at the end of the third year
Now, we can find the cost of the machine at the end of each year.

1. **Cost after Year 1**:
\[ \text{Cost after Year 1} = 40000 - 4000 = 36000 \]

2. **Cost after Year 2**:
\[ \text{Cost after Year 2} = 36000 - 3600 = 32400 \]

3. **Depreciation in Year 3**:
\[ \text{Depreciation in Year 3} = 10\% \text{ of } 32400 = 0.10 \times 32400 = 3240 \]

4. **Cost after Year 3**:
\[ \text{Cost after Year 3} = 32400 - 3240 = 29160 \]

### Final Answers:
1. Rate of Depreciation: **10%**
2. Original Cost of the Machine: **₹40,000**
3. Cost at the End of the Third Year: **₹29,160**