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The ratio of the number of students studying in schools A, B and C is 6:8:7 respectively, if the number of students studying in each of the schools is increased 20%, 15% and 20% respectively, then what will be the new ratio of the number of the students in school A, B and C?

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An Intiative by Sri Chaitanya

18:23:21

16:28:30

20:12:36

22:21:12

answer is A.

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Detailed Solution

Concept- Finding a new ratio of students
Assuming the number of students in school A =

6 x

The number of students in school B =

8 x

The number of students in school C =

7 x

Given that the percentage in A, B and C has increased by 20%, 15% and 20% respectively.
For school A,
Total number of students in school A

= 6 x + 20 % of 6 x

= 6 x + \frac{20}{100} \times 6 x

= 6 x + \frac{6 x}{5}

= \frac{36 x}{5}

For school B,
Total number of students in school B

= 8 x + 15 % of 8 x

= 8 x + \frac{15}{100} \times 8 x

= 8 x + \frac{2 x \times 3}{5}

= \frac{40 x + 6 x}{5}

= \frac{46 x}{5}

For school C,
Total number of students in school c

= 7 x + 20 % of 7 x

= 7 x + \frac{20}{100} \times 7 x

= 7 x + \frac{7 x}{5}

= \frac{35 x + 7 x}{5}

= \frac{42 x}{5}

Therefore, the new ratio of the number of students in A, B, C schools,

\Rightarrow \frac{36 x}{5} : \frac{46 x}{5} : \frac{42 x}{5}

= 36 x : 46 x : 42 x

= 18 : 23 : 21

Hence, the correct answer is option 1.

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