Question

The ratio of boys and girls in a class is 5:3. 20% of the boys and 60% of the girls have passed in a class. What percentage of class has passed in first class?

Answer 1

Hint: Consider the number of boys as 5x and number of girls as 3x because now the ratio of number of boys and number of girls is also 5:3. We know that the formula for percentage of students passed in first class is the number of students passed in first class divided by total number of students and the whole multiplied by 100.

Complete step-by-step solution -
Given, the ratio of boys and girls in a class is \[5:3\]
Let number of boys be 5x . . . . . . . . . . . . . . . . .(1)
      Number of girls be 3x . . . . . . . . . . . . . . . . . .(2)
Given, 20% of boys and 60% of girls have passed in a class
So, number of those who passed in first class is given by
=$20\% \text{of}\ \text{5x} + 60\% \text{of}\ \text{3x} $
$=\left( \dfrac{20}{100}\times 5x \right)+\left( \dfrac{60}{100}\times 3x \right) $
$=x+\dfrac{9x}{5} $
$=\dfrac{14x}{5} $. . . . . . . . . . . . . . . .(3)
So, number of boys and girls who passed in first class \[=\dfrac{14x}{5}\]
We have to find to find percentage of class who passed in first class =no, of students passed in first class and multiplied by 100/number of students in total class
$=\left( \dfrac{14x}{5}\times \dfrac{1}{5x+3x}\times 100 \right)\% $
$=\dfrac{14x}{5}\times \dfrac{100}{8x}\% $
\[=35\% \]
So, the percentage of the class who passed in first class $ =35\% $

Note: Percentages are widely used in many different areas. The word percent means per hundred. It is used for discounts in shops, bank interest rates and marks obtained. We will all calculate this in terms of percentage. It is used in a literacy rate calculated to know how many students are pursuing education per 100 students in the population.