The average age of students of aclass is 15.8yr. The average age of boys in the class is 16.4yr and that of the girls is 15.4 yr. Find out the ratio of the number of boys to the number of girls in the class

Options

A. `3:1`
B. `5:2`
C. `2:3`
D. `3:7`

Answer

To find the ratio of the number of boys to the number of girls in the class based on the given average ages, we can use the method of alligation. Here’s a step-by-step solution:

### Step 1: Identify the given averages
- Average age of the class (A) = 15.8 years
- Average age of boys (B) = 16.4 years
- Average age of girls (G) = 15.4 years

### Step 2: Set up the alligation
We will use the alligation method to find the ratio of boys to girls. The formula for alligation is as follows:

\[ \text{Ratio of boys to girls} = \frac{G - A}{B - A} \]

### Step 3: Calculate the differences
- Difference between the average age of girls and the class average:
\[ G - A = 15.4 - 15.8 = -0.4 \]
- Difference between the average age of boys and the class average:
\[ B - A = 16.4 - 15.8 = 0.6 \]

### Step 4: Set up the ratio
Now, we can substitute these values into the ratio:
\[ \text{Ratio of boys to girls} = \frac{-0.4}{0.6} = \frac{0.4}{0.6} \]

### Step 5: Simplify the ratio
To simplify the ratio:
\[ \frac{0.4}{0.6} = \frac{4}{6} = \frac{2}{3} \]

### Step 6: State the final answer
Thus, the ratio of the number of boys to the number of girls in the class is:
\[ \text{Ratio of boys to girls} = 2:3 \]