The population of a state is counted after every three years. It is found that population each time is increased by `20%` as compared to the previous count. If the population in the year 1998 was 42 lakh. What will be the population in the year 2007?

Options

A. 60. 48 lakh
B. 72. 576 lakh
C. 62. 576 lakh
D. 70. 48 lakh

Answer

To find the population of the state in the year 2007, given that the population increases by 20% every three years, we can follow these steps:

### Step 1: Identify the initial population
The population in the year 1998 is given as 42 lakh.

### Step 2: Calculate the population for the year 2001
To find the population in 2001, we need to calculate a 20% increase on the population of 1998.

\[ \text{Population in 2001} = \text{Population in 1998} + 20\% \text{ of Population in 1998} \]

Calculating 20% of 42 lakh:
\[ 20\% \text{ of } 42 = \frac{20}{100} \times 42 = 8.4 \text{ lakh} \]

Now, add this to the initial population:
\[ \text{Population in 2001} = 42 + 8.4 = 50.4 \text{ lakh} \]

### Step 3: Calculate the population for the year 2004
Next, we calculate the population for the year 2004, which is another 20% increase on the population of 2001.

\[ \text{Population in 2004} = \text{Population in 2001} + 20\% \text{ of Population in 2001} \]

Calculating 20% of 50.4 lakh:
\[ 20\% \text{ of } 50.4 = \frac{20}{100} \times 50.4 = 10.08 \text{ lakh} \]

Now, add this to the population in 2001:
\[ \text{Population in 2004} = 50.4 + 10.08 = 60.48 \text{ lakh} \]

### Step 4: Calculate the population for the year 2007
Finally, we calculate the population for the year 2007, which is another 20% increase on the population of 2004.

\[ \text{Population in 2007} = \text{Population in 2004} + 20\% \text{ of Population in 2004} \]

Calculating 20% of 60.48 lakh:
\[ 20\% \text{ of } 60.48 = \frac{20}{100} \times 60.48 = 12.096 \text{ lakh} \]

Now, add this to the population in 2004:
\[ \text{Population in 2007} = 60.48 + 12.096 = 72.576 \text{ lakh} \]

### Final Answer
Thus, the population in the year 2007 is **72.576 lakh**.

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