Question

The total number of students in class is 35. If the number of girls is two-fifths of the number of boys. find the number of girls?
\[a)7\]
\[b)5\]
\[c)10\]
\[d)15\]

Answer 1

Hint: We should try to assume the unknown value and then we will find the all-possible relation. In these types of questions, it would be easy if we solve it using two variable equations. Two variable equations can be solved by using a substitution method. Assume some variables to boys and other to girls say x and y.

Complete step-by-step answer:
We first assume the number of boys to be x. and the number of girls to be y.
So, by above relation
y=two-fifth of x
 $ y = \dfrac{2}{5} \times x $
We have given the total no of students is\[35\],
So, number of boys +number of girls=\[35\]
 $ x + \dfrac{2}{5}x = 35 $
Taking LCM of 5 and 1,
 $ \dfrac{{5x + 2x}}{5} = 35 $
 $ \dfrac{{7x}}{5} = 35 $
Solving for the value of x
 $ x = \dfrac{{35 \times 5}}{7} $
 $ x = 25 $
The number of girls is $ \dfrac{2}{5} \times x $
 $ = \dfrac{2}{5} \times 25 $
 $ = 10 $
The number of girls in class is 10.
So, the correct answer is “Option C”.

Note: We can also solve two variable equations by elimination method. To do the elimination method we have to follow these steps: Try to Find the variable that cancels out. To cancel a variable, we can either add or subtract both equations. if a variable does not cancel out, multiply one equation by some constant so a variable will cancel out. then combine two equations, add the left sides together, and add the right sides together. If you set your equation up right, one of the variables should cancel. Solve for the last variable.