Question

If 60% of the students in a school are boys and numbers of girls be 660 the numbers of boys are:

• A. 990
• B. 890
• C. 1650
• D. 1550

Hint:

Using ratios simplifies percentage problems. Since Boys : Girls = $60% : 40% = 3 : 2$, and 2 units correspond to 660, then 1 unit is 330, and 3 units (boys) must be $3 \times 330 = 990$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a percentage-based algebraic problem.
The total student population in a school can be represented as $100%$.
The total population is divided into two mutually exclusive categories: boys and girls.
Key Formula or Approach:
If the percentage of boys is given as $B%$, the percentage of girls ($G%$) is: \[ G% = 100% - B% \] Once the percentages are established, we can construct a proportion: \[ \text{Number of Boys} = \frac{\text{Percentage of Boys}}{\text{Percentage of Girls}} \times \text{Number of Girls} \]

Step 2: Detailed Explanation:
Given:
- Percentage of boys = $60%$
- Therefore, the percentage of girls is: \[ 100% - 60% = 40% \] - The actual number of girls is given as $660$.
Let the total number of students in the school be $T$.
Since $40%$ of the total students are girls, we can write: \[ 40% \text{ of } T = 660 \] \[ \frac{40}{100} \cdot T = 660 \] \[ 0.4 \cdot T = 660 \] Solve for $T$: \[ T = \frac{660}{0.4} = 1650 \] The total number of students is $1650$.
Now, calculate the number of boys, which is $60%$ of the total: \[ \text{Number of Boys} = 60% \text{ of } 1650 \] \[ \text{Number of Boys} = \frac{60}{100} \cdot 1650 \] \[ \text{Number of Boys} = 0.6 \cdot 1650 = 990 \] Alternatively, using direct ratios: \[ \text{Number of Boys} = \frac{60}{40} \times 660 = \frac{3}{2} \times 660 = 3 \times 330 = 990 \]

Step 3: Final Answer:
The total number of boys in the school is 990.