Question

The number of boys and girls in a class are in ratio \[7:5\]. The number of boys is 8 more than the number of girls. What is the total class strength?

Answer 1

Hint: Assume number of boys and girls as two different variables. We use the concept of ratio to write the given ratio in the form of a fraction and form an equation. Using the second condition write another equation. Use a substituting method to find the number of girls and boys in a class and take a sum to calculate the strength of the class.
* Ratio of any number ‘x’ to ‘y’ is given by \[x:y = \dfrac{x}{y}\]

Complete step-by-step solution:
Let us assume the number of boys in class as ‘x’ and number of girls in class as ‘y’.
We are given that number of boys and girls in a class are in ratio\[7:5\].
Then using the concept of ratio we can write \[\dfrac{x}{y} = \dfrac{7}{5}\]
Cross multiply the values from both sides of the equation to opposite side of the equation
\[ \Rightarrow 5x = 7y\]...................… (1)
Also, we are given that number of boys is 8 more than the number of girls
So number of boys will be equal to number of girls if 8 is added to the number of girls
\[ \Rightarrow x = y + 8\]..............… (2)
Substitute the value of ‘x’ from equation (2) in equation (1)
\[ \Rightarrow 5(y + 8) = 7y\]
Calculate the product in LHS of the equation
\[ \Rightarrow 5y + 40 = 7y\]
Bring all terms with variable to one side of the equation
\[ \Rightarrow 40 = 7y - 5y\]
\[ \Rightarrow 40 = 2y\]
Divide both sides of the equation by 2
\[ \Rightarrow \dfrac{{40}}{2} = \dfrac{{2y}}{2}\]
Cancel same factors from numerator and denominator on both sides of the equation
\[ \Rightarrow y = 20\]
Substitute the value of ‘y’ in equation (2) to calculate the value of ‘x’
\[ \Rightarrow x = 20 + 8\]
\[ \Rightarrow x = 28\]
\[ \Rightarrow \]Number of boys in class is 28 and number of girls in class is 20
\[ \Rightarrow \]Total number of students in class \[ = x + y\]
Substitute the value of x and y
\[ \Rightarrow \]Total number of students in class \[ = 28 + 20\]
\[ \Rightarrow \]Total number of students in class \[ = 48\]

\[\therefore \]Strength of class is 48.

Note: Many students make mistakes in forming an equation with a second condition and end up adding the value of 8 on the wrong side of the equation, keep in mind we add the value by which one variable is greater than the other variable on that side which has lesser value.