Number of boys in a school are 360 and the rest are girls. If the total strength of the school is 750, find the ratio of :
a. the number of boys to the number of girls.
b. the number of girls to the number of boys.
c. the number of boys to all students in the school.
d. all students in the school to the number of girls.

Answer

To solve the problem step by step, we will find the required ratios as per the question.

**Given:**
- Number of boys = 360
- Total strength of the school = 750

**Step 1: Calculate the number of girls.**
To find the number of girls, we subtract the number of boys from the total strength.

\[ \text{Number of girls} = \text{Total strength} - \text{Number of boys} = 750 - 360 = 390 \]

**Step 2: Find the ratio of the number of boys to the number of girls (Part a).**
The ratio of boys to girls is given by:

\[ \text{Ratio of boys to girls} = \frac{\text{Number of boys}}{\text{Number of girls}} = \frac{360}{390} \]

To simplify this ratio, we can divide both the numerator and the denominator by 30:

\[ \frac{360 \div 30}{390 \div 30} = \frac{12}{13} \]

Thus, the ratio of boys to girls is **12:13**.

**Step 3: Find the ratio of the number of girls to the number of boys (Part b).**
The ratio of girls to boys is given by:

\[ \text{Ratio of girls to boys} = \frac{\text{Number of girls}}{\text{Number of boys}} = \frac{390}{360} \]

To simplify this ratio, we can divide both the numerator and the denominator by 30:

\[ \frac{390 \div 30}{360 \div 30} = \frac{13}{12} \]

Thus, the ratio of girls to boys is **13:12**.

**Step 4: Find the ratio of the number of boys to all students in the school (Part c).**
The ratio of boys to all students is given by:

\[ \text{Ratio of boys to all students} = \frac{\text{Number of boys}}{\text{Total strength}} = \frac{360}{750} \]

To simplify this ratio, we can divide both the numerator and the denominator by 30:

\[ \frac{360 \div 30}{750 \div 30} = \frac{12}{25} \]

Thus, the ratio of boys to all students is **12:25**.

**Step 5: Find the ratio of all students in the school to the number of girls (Part d).**
The ratio of all students to girls is given by:

\[ \text{Ratio of all students to girls} = \frac{\text{Total strength}}{\text{Number of girls}} = \frac{750}{390} \]

To simplify this ratio, we can divide both the numerator and the denominator by 30:

\[ \frac{750 \div 30}{390 \div 30} = \frac{25}{13} \]

Thus, the ratio of all students to girls is **25:13**.

**Final Answers:**
a. Ratio of boys to girls = **12:13**
b. Ratio of girls to boys = **13:12**
c. Ratio of boys to all students = **12:25**
d. Ratio of all students to girls = **25:13**

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