Question

In a class the number of students is 84. If there were six boys more and six girls less then the ratio of boys and girls is 5 : 2. Find the number of boys in the class.

• A. 60
• B. 54
• C. 51
• D. 56

Answer 1

The correct option is B 54

Let number of girls be x and number of boys be y, the equation formed will be as follows

$x+y=84-------------\left(1\right)$

The ratio given as per question is

$\frac{y+6}{x-6}=\frac{5}{2}$

Using cross-multiplication to solve the ratio, we get

$2(y+6)=5(x-6)$

$=2y+12=5x-30$

$=5x-2y=42----------\left(2\right)$

multiplying equation (1) by 5 and subtracting from (2),we get

$=5x-2y-5x-5y=42-420$

$=-7y=378$

$⟹y=\frac{378}{7}=54$

Number of boys$=y=54$

So, option (b) is correct.