The total number of students in a school is 31700. If the ratio of boys to the girls in the school is 743 : 842, what is the total number of girls in the school?

Correct option is C

Given:

1. Total number of students = 31,700

2. The ratio of boys to girls = 743 : 842

3. We need to calculate the total number of girls.

Formula Used:

The total number of students is divided in proportion to the given ratio:

$$\text{Total Students} = \text{Boys} + \text{Girls}$$​

$$\text{Girls} = \frac{\text{Ratio of Girls}}{\text{Sum of Ratios}} \times \text{Total Students}$$​

Solution:

1. Find the sum of the ratio terms:

Sum of Ratios = 743 + 842 = 1585

2. Calculate the total number of girls:

$$\text{Girls} = \frac{\text{Ratio of Girls}}{\text{Sum of Ratios}} \times \text{Total Students}$$​

Substitute the values:

$$\text{Girls} = \frac{842}{1585} \times 31,700$$​

3. Simplify:

$$\text{Girls} = \frac{842 \times 31,700}{1585}$$​

$$\text{Girls} = \frac{26,711,400}{1585} = 16,840$$​

Final Answer:

The total number of girls in the school is 16,840.