The income of a company in creases `20%` per year. If the income is `Rs. 26,64,000` in the year 2012, then its income in the year 2010 was :

Options

A. `Rs. 28,55,000 `
B. `Rs. 18,50.000 `
C. `Rs. 28,20,000`
D. `Rs. 21,20,000`

Answer

To find the income of the company in the year 2010, we need to work backwards from the income in 2012, which is Rs. 26,64,000. Since the income increases by 20% each year, we can use the formula for compound interest to find the income for previous years.

### Step-by-Step Solution:

1. **Identify the Income for 2012**:
The income in 2012 is given as Rs. 26,64,000.

2. **Calculate the Income for 2011**:
To find the income for 2011, we need to divide the income for 2012 by 1 plus the rate of increase (20% or 0.20).
\[ \text{Income in 2011} = \frac{\text{Income in 2012}}{1 + \text{Rate of Increase}} = \frac{26,64,000}{1.20} \]
\[ \text{Income in 2011} = \frac{26,64,000}{1.20} = 22,20,000 \]

3. **Calculate the Income for 2010**:
Now, we will find the income for 2010 by applying the same method to the income for 2011.
\[ \text{Income in 2010} = \frac{\text{Income in 2011}}{1 + \text{Rate of Increase}} = \frac{22,20,000}{1.20} \]
\[ \text{Income in 2010} = \frac{22,20,000}{1.20} = 18,50,000 \]

4. **Final Result**:
Therefore, the income of the company in the year 2010 was Rs. 18,50,000.

### Summary of the Solution:
- Income in 2012: Rs. 26,64,000
- Income in 2011: Rs. 22,20,000
- Income in 2010: Rs. 18,50,000