In the famous Bhojpur island, there are four men for every three women and five children for every three men. How many children are there in the island if it has 531 women?

Options

A. 454
B. 1180
C. 1070
D. 389

Answer

To solve the problem step by step, we will analyze the ratios given in the question and use them to find the number of children on Bhojpur island.

### Step 1: Understand the Ratios
We know that:
- The ratio of men to women is 4:3.
- The ratio of children to men is 5:3.

### Step 2: Set Up the Ratios
Let's denote:
- The number of men as \( M \)
- The number of women as \( W \)
- The number of children as \( C \)

From the ratios, we can express \( M \) and \( C \) in terms of \( W \):
- From the ratio of men to women (4:3), we can write:
\[ \frac{M}{W} = \frac{4}{3} \implies M = \frac{4}{3}W \]

- From the ratio of children to men (5:3), we can write:
\[ \frac{C}{M} = \frac{5}{3} \implies C = \frac{5}{3}M \]

### Step 3: Substitute the Number of Women
We are given that there are 531 women on the island:
\[ W = 531 \]

### Step 4: Calculate the Number of Men
Substituting \( W \) into the equation for \( M \):
\[ M = \frac{4}{3} \times 531 = \frac{4 \times 531}{3} = \frac{2124}{3} = 708 \]

### Step 5: Calculate the Number of Children
Now, substitute \( M \) into the equation for \( C \):
\[ C = \frac{5}{3} \times 708 = \frac{5 \times 708}{3} = \frac{3540}{3} = 1180 \]

### Conclusion
Thus, the number of children on Bhojpur island is:
\[ C = 1180 \]

### Final Answer
The number of children on Bhojpur island is **1180**.

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