Question

The ratio of the number of boys and girls in a school is 3:2. If 20% of the boys and 25% of the girls are scholarship holders, what percentage of the students do not get the scholarship?
A) 56%
B) 70%
C) 78%
D) 80%

Answer 1

Hint: Apply the rules of percentage values as per the ratio of boys versus girls as given and equate. In this case we will apply the same to compare the quantities of boys and girls and get the solution.
Complete step by step solution:
A ratio is the comparison or simplified form of two quantities of the same kind. This relation indicates how many times one quantity is equal to the other; or in other words, ratio is a number, which expresses one quantity as a fraction of the other.
Proportion is an equation which defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios. In proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
Let total number of students
= 100
Ratio of boys and girls
= 3:2
Number of boys
= \[\dfrac{3}{5}\,\times 100\]
= 60
Number of girls
= 100 − 60
= 40
Number of boy students holding the scholarship
= 20 % of 60
\[=\dfrac{20}{100}\times 60=12\]
Number of girl students holding a scholarship
= 25 % of 40
\[=\dfrac{25}{100}\times 40=10\]
Total number of students holding the scholarship
= 12+10
= 22
Number of students who do not get a scholarship
= 100 − 22
= 78
Required percentage
\[=\dfrac{78}{100}\times 100=78%\]
The answer is C.

Note: Substitute the appropriate values and work out to get the resulting total percentage of students who don’t get a scholarship accordingly. Simple operations like addition, subtraction and reducing a fraction should be done with precision and accuracy.