Question

The total number of students in a school is$130$. The ratio of girls to boys is$2:3$. Find the ratio of:

(i) the number of boys to the total number of students.

(ii) the total number of students to the number of girls.

Answer 1

Step 1: Find the sum of terms of the ratio

The ratio of girls and boys = $2:3$

Sum of terms = $2+3=5$

Step 2: Find the number of boys and girls

Total number of students in school = $130$

Number of girls = $130\times \frac{2}{5}=26\times 2=52$

Number of boys = $130\times \frac{3}{5}=26\times 3=78$

Step 3: Find the ratio

(i) Ratio between the number of boys to the total number of students = $\frac{78}{130}=\frac{78÷26}{130÷26}=\frac{3}{5}=3:5$

(ii) Ratio between the total number of students to the number of girls = $\frac{130}{52}=\frac{130÷26}{52÷26}=\frac{5}{2}=5:2$

Hence, the ratio between the number of boys to the total number of students is$3:5$, and the ratio between the total number of students to the number of girls is$5:2$.