In a town, 80% of the population are adults of which the men and women are in the ratio of 9 : 7, re- spectively. If the number of adult women is 4.2 lakh, what is the total population of the town?

Options

A. 12 lakh
B. 9.6 lakh
C. 9.8 lakh
D. 11.6 lakh

Answer

To solve the problem step by step, we will follow the given information and use basic arithmetic to find the total population of the town.

### Step 1: Understand the ratio of men and women
We know that the ratio of men to women is 9:7. This means for every 9 men, there are 7 women.

### Step 2: Identify the number of adult women
The problem states that the number of adult women is 4.2 lakh (or 420,000).

### Step 3: Set up the ratio
Let the number of men be represented as \( M \) and the number of women as \( W \). According to the ratio, we can express the number of men in terms of women:
\[ \frac{M}{W} = \frac{9}{7} \]
From this, we can express \( M \) as:
\[ M = \frac{9}{7} \times W \]

### Step 4: Substitute the number of women
Now, substitute \( W = 4.2 \) lakh into the equation:
\[ M = \frac{9}{7} \times 4.2 \]

### Step 5: Calculate the number of men
Calculating \( M \):
\[ M = \frac{9 \times 4.2}{7} = \frac{37.8}{7} = 5.4 \text{ lakh} \]
So, the number of men is 5.4 lakh.

### Step 6: Calculate the total number of adults
Now, we can find the total number of adults (men + women):
\[ \text{Total Adults} = M + W = 5.4 \text{ lakh} + 4.2 \text{ lakh} = 9.6 \text{ lakh} \]

### Step 7: Relate adult population to total population
We know that the adult population (9.6 lakh) represents 80% of the total population. Let the total population be \( P \):
\[ 0.8P = 9.6 \text{ lakh} \]

### Step 8: Solve for total population
To find \( P \), we rearrange the equation:
\[ P = \frac{9.6 \text{ lakh}}{0.8} = 12 \text{ lakh} \]

### Conclusion
The total population of the town is **12 lakh**.

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