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The number of students in three classes is in the ratio $3:13:6$. If $18$ students are added to each class, the ratio changes to $15:35:21$.

The total number of students in all the three classes in the beginning was:

1. $22$
2. $66$
3. $88$
4. $110$

Let the three classes have $3x$, $13x$ and $6x$ students respectively. $18$ students are added in each class.

After that $3x+18,13x+18$ and $6x+18$ are the number of students in each class.

Given, $3x+18: 13x+18 : 6x+18 = 15:35:21$

$\implies \frac{3x+18}{6x+18}=\frac{15}{21}$

$\implies \frac{x + 6}{2x + 6} = \frac{5}{7}$

$\implies 7x + 42 = 10x + 30$

$\implies 3x = 12$

$\implies x = 4$

So, the total number of students in all the three classes, in the beginning, $=3*4+13*4+6*4=88.$

Option (C) is the correct answer.

a small correction bro..

it’s $15:35: 31 21$

and a suggestion it’s better to use $3x~and~6x$,  from calculation perspective it’ll be more easy to solve.

$\frac{3x+18}{6x + 18} = \frac{15}{21} \Rightarrow \frac{x+6}{2x + 6} = \frac{5}{7}$

Corrected👍
Let number of students in each classes be 3k,13k,6k so that their ratio is 3:13:6.

if we add 18 students to each class we have 3k+18,13k+18,6k+18 students in each class.

But it’s ratio is given as 15:35:21.

So ,3k+18:13k+18:6k+18=15:35:21.

This implies,(3k+18)/(13k+18)=15/35

=>(3k+18)*7=(13k+18)*3

=>21k+18*7=39k+18*3

=>18*4=18k

=>k=4.

So total number of students are 3k+13k+6k=22*k=22*4=88