GATE CSE 2021 Set 2 | GA Question: 8

Question

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:

• A. $22$
• B. $66$
• C. $88$
• D. $110$

Answer 1

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.

Comments

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.

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

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Corrected👍

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@Lakshman Bhaiya @Nikhil_dhama Can someone please point out what I am doing wrong in below approach:

let total students be x in the beginning.

students in one class=3x/22

add 18 more students 3x/22 +18

(eqn 1)

now this should be equal to final students in that class i.e.                  15*(x+18*3)/71 (eqn 2)where x+54 is the total number of students after increase.

equate eqn1 and 2 but I am getting 94.1 as x.

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What you are doing is calculation mistake, solve eqn1 and eqn2, you will get x=88.
$\frac{3}{22}x + 18 = \frac{15}{71}(x + 54) \implies (x + 6*22)*71 = 22*5(x+54)$

Answer 2

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