Question

The ratio of numbers of students studying Arts, Commerce and Science in a college is \[3:5:8\]. What is the new ratio of the number of students studying Arts, Commerce and Science respectively, if there is an increase of \[20%,\ 40%\ and\ 25%\] in the numbers of students studying Arts, Commerce and Science.
A) \[35:18:50\]
B) \[18:50:35\]
C) \[20:18:50\]
D) \[18:35:50\]

Answer 1

Hint: In order to solve the question, first we will let the common ratio be ‘x’. then the numbers of students studying arts, commerce and science will be 3x, 5x and 8x respectively. Then we will find the increase in the number of students of arts, commerce and science and find the new required ration of the number of students studying arts, commerce and science. In this way we will get the required ratio after the increase in the number of students.

Complete step by step solution:
We have given that,
The ratio of numbers of students studying Arts, Commerce and Science in a college is \[3:5:8\].
Thus,
Arts, Commerce and Science =\[3:5:8\]
Let the common ratio be ‘x’.
Therefore,
Number of students studying arts = \[3x\]
Number of students studying commerce = \[5x\]
Number of students studying science = \[8x\]
Now,
\[\Rightarrow \]Increase in the arts students is \[20%\].
New numbers of students studying arts = \[3x+\left( 3x\times \dfrac{20}{100} \right)=3x+\dfrac{60x}{100}=\dfrac{360x}{100}\].
\[\Rightarrow \]Increase in the commerce students is \[40%\].
New numbers of students studying arts = \[5x+\left( 5x\times \dfrac{40}{100} \right)=5x+\dfrac{200x}{100}=\dfrac{700x}{100}\].
\[\Rightarrow \]Increase in the science students is \[25%\].
New numbers of students studying arts = \[8x+\left( 8x\times \dfrac{25}{100} \right)=8x+\dfrac{200x}{100}=\dfrac{1000x}{100}\].
Therefore,
New ratio will be,
Arts, Commerce and Science =\[\dfrac{360x}{100}:\dfrac{700x}{100}:\dfrac{1000x}{100}=36x:70x:100x=18:35:50\]
Arts, Commerce and Science =\[18:35:50\]

Hence the correct answer is option ‘D’

Note: While solving this question substitutes the appropriate values and work out to get the resulting total percentage of students after the increase in the number of students. Simple operations like addition, subtraction and reducing the fraction should be done with precision and accuracy to avoid making any type of calculation error.