Depreciation Calculation:
To calculate the effective life of the machine, we need to understand how the depreciation is calculated. In this case, the machine is depreciated at the rate of 20% on the reducing balance method.

The Reducing Balance Method:
The reducing balance method is a common method used to calculate depreciation. It takes into account the decreasing value of an asset over time. In this method, the depreciation expense is calculated as a fixed percentage of the net book value of the asset.

Step 1: Calculate the Depreciation Expense:
The first step is to calculate the depreciation expense for each year. In this case, the depreciation rate is 20% and the original cost of the machine is Rs. 100,000. The formula to calculate the depreciation expense is:

Depreciation Expense = Depreciation Rate * Net Book Value

For the first year, the net book value is the original cost of the machine. Therefore, the depreciation expense for the first year is:

Depreciation Expense Year 1 = 20% * Rs. 100,000 = Rs. 20,000

Step 2: Calculate the Net Book Value:
The net book value is the original cost of the machine minus the accumulated depreciation. It represents the value of the machine at a given point in time. The formula to calculate the net book value is:

Net Book Value = Original Cost - Accumulated Depreciation

For the first year, the accumulated depreciation is equal to the depreciation expense. Therefore, the net book value at the end of the first year is:

Net Book Value Year 1 = Rs. 100,000 - Rs. 20,000 = Rs. 80,000

Step 3: Calculate the Accumulated Depreciation:
The accumulated depreciation is the sum of the depreciation expense for each year. It represents the total depreciation over the life of the asset. The formula to calculate the accumulated depreciation is:

Accumulated Depreciation = Depreciation Expense Year 1 + Depreciation Expense Year 2 + ... + Depreciation Expense Year N

In this case, we need to calculate the accumulated depreciation until the net book value reaches the ultimate scrap value of Rs. 30,000.

Step 4: Determine the Effective Life:
The effective life of the machine is the number of years it takes for the net book value to reach the ultimate scrap value. Since we know the depreciation expense for each year, we can calculate the effective life by dividing the net book value by the depreciation expense.

Effective Life = Net Book Value / Depreciation Expense

In this case, the net book value is Rs. 30,000 and the depreciation expense is Rs. 20,000. Therefore, the effective life of the machine is:

Effective Life = Rs. 30,000 / Rs. 20,000 = 1.5 years

Conclusion:
The effective life of the machine is 1.5 years. This means that it will take 1.5 years for the net book value of the machine to reach the ultimate scrap value of Rs. 30,000. The reducing balance method of depreciation allows for a faster depreciation in the initial years, which reflects the decreasing value of the asset over time.