Question

The number of girls in a class is 5 times the number of boys. Which of the following cannot be the total number of children in the class?
(a) 24
(b) 30
(c) 35
(d) 42

Answer 1

Hint:To solve this question, we have to make an assumption that the number of boys in class be x, and then we can say that the number of girls in class will be 5x. So,
The number of boys + The number of girls = Total number of children,
That is, x + 5x = Total number of children
Or, we can say, 6x = Total number of children.
Now, we will find the value of x by putting the options as the total number of children. The option at which we will get a fractional number will be the correct answer.

Complete step-by-step answer:
In this question, we are given that the number of girls in the class is 5 times the number of boys. And then we have to find which of the following is not the possible strength of the class. Let us consider that the number of boys in the class is x and we have been given that the number of girls is 5 times the number of boys in the class. So, we can say the number of girls in the class is 5x.
Now we can say that the total number of children in the class is equal to the sum of the number of boys and the number of girls, that is,
Total number of children = x + 5x
Total number of children = 6x
Now, we will put different values of the total number of children to get the value of x. And we check for which value of the total number of children we get the value of x as a fractional number.
So, for the total number of children = 24, we will get
24 = 6x
x = 4
So, 24 can be the total number of children in the class. Now, for the total number of children = 30, we will get,
30 = 6x
x = 5 which means that 30 can also be the total number of children in the class.
Now, for the total number of children = 42, we will get
42 = 6x
x = 7, which means that 42 can also be the total number of children in the class.
Now, for the total number of children = 35, we will get
35 = 6x
\[x=\dfrac{35}{6}\]
Here we get a fractional value of x which means that 35 cannot be the total number of children in the class.
Therefore, option (c) is the right answer.

Note: A linear equation in one variable is an equation that can be written in the form ax + b =0 , where a and b are real numbers and linear equations are also first-degree equations because the exponent on the variable is understood to be 1.In this question, the possible mistake one can make is by equating the total number of children to 5x, that is the number of girls and the class contains both girls and boys. So, there are chances of getting the wrong answer.