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

Options

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

Answer

To solve the problem, we need to find the number of children on Mauritius Island based on the given ratios of men, women, and children. Let's break it down step by step.

### Step 1: Understand the Ratios
We know from the problem:
- There are 4 men for every 3 women.
- There are 5 children for every 3 men.

### Step 2: Set Up the Ratios
Let:
- The number of women (W) = 531 (given)
- The number of men (M) can be expressed in terms of women using the ratio of men to women:
\[ \frac{M}{W} = \frac{4}{3} \implies M = \frac{4}{3} W \]

### Step 3: Calculate the Number of Men
Substituting W = 531 into the equation for M:
\[ M = \frac{4}{3} \times 531 = \frac{4 \times 531}{3} = \frac{2124}{3} = 708 \]
So, there are 708 men on the island.

### Step 4: Relate Children to Men
Now, we can express the number of children (C) in terms of men using the ratio of children to men:
\[ \frac{C}{M} = \frac{5}{3} \implies C = \frac{5}{3} M \]

### Step 5: Calculate the Number of Children
Substituting M = 708 into the equation for C:
\[ C = \frac{5}{3} \times 708 = \frac{5 \times 708}{3} = \frac{3540}{3} = 1180 \]
Thus, there are 1180 children on the island.

### Final Answer
The total number of children on Mauritius Island is **1180**.

---