Question

In a school, a class has 40 students out of which x are girls. If the product of the number of girls and number of boys in the class is 375; the number of boys in the class is ______.

Options

• 15

• 25

• 15 or 25

• 15 and 25

Answer 1

In a school, a class has 40 students out of which x are girls. If the product of the number of girls and number of boys in the class is 375; the number of boys in the class is 15 or 25.

Explanation:

Total no. of students in a class = 40

No. of girls = x

∴ No. of boys = 40 – x

According to given condition,

x(40 – x) = 375

`\implies` 40x – x² – 375 = 0

`\implies` x² – 40x + 375 = 0

`\implies` x² – 15x – 25x + 375 = 0

`\implies` x(x – 15) – 25(x – 15) = 0

`\implies` (x – 15)(x – 25) = 0

Either x – 15 = 0 or x – 25 = 0

`\implies` x = 15 or x = 25

`\implies` x = 15 or 25

When x = 15;

No. of boys = 40 – x

= 40 – 15

= 25

When x = 25;

No. of boys = 40 – x

= 40 – 25

= 15