GATE CS 2021 Set 2 Q.8 (GA Q.8): Quantitative Aptitude

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:

110

Official answer and solution

Official answer: C
From: Official GATE 2021 answer key

Solution

Set up proportional equations from the given ratios before and after adding students.

Let the initial numbers of students in the three classes be $3k$ , $13k$ , and $6k$ , where $k$ is a positive constant. The initial total number of students is:

\text{Total} = 3k + 13k + 6k = 22k

After adding 18 students to each class, the new counts are $3k + 18$ , $13k + 18$ , and $6k + 18$ , and their ratio is $15 : 35 : 21$ .

Comparing the first and third classes:

\frac{3k + 18}{6k + 18} = \frac{15}{21} = \frac{5}{7}

7(3k + 18) = 5(6k + 18) \implies 21k + 126 = 30k + 90 \implies 9k = 36 \implies k = 4

Checking with the second class: $13(4) + 18 = 70$ . Since $30 : 70 : 42 = 15 : 35 : 21$ , the solution is consistent.

The initial total number of students was $22k = 22 \times 4 = 88$ .

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2021 Computer Science and Information Technology - Session 2 (CS2)
Question: 8 of 65, printed as GA Q.8
Section: General Aptitude

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