Multiple Choice Questions

The ratio of the number of students in Science to that in Humanities in Grade 12 of 360 students is ...........

Quantitative Aptitude (MTS) Ratio, Proportion

The ratio of the number of students in Science to that in Humanities, in Grade 12 of 360 students, is 2 : 3. When some new

students are admitted, the number of Science students increase by 18 and the ratio of the Science students to Humanities

students changes to 3 : 5. What is the number of new Humanities students admitted?

This questions was previously asked in

SSC MTS 20th October 2021 Shift-3

- Initially, the ratio of Science to Humanities students is 2:3. With 360 students in total, this means there are:

- $2 x$ Science students

- $3 x$ Humanities students

- Since $2 x + 3 x = 360$ , then $x = 72$ .

- Science students = $2 \times 72 = 144$

- Humanities students = $3 \times 72 = 216$

- After admitting 18 new Science students, the number of Science students is 162.

- The new ratio of Science to Humanities is 3:5. Let the new number of Humanities students be $H + y$ .

- Hence, the ratio becomes:

- $162 / (216 + y) = 3 / 5$

- Solving, we get:

- $5 \times 162 = 3 \times (216 + y)$

- $810 = 648 + 3 y$

- $162 = 3 y$

- $y = 54$

- Answer: Option 1, 54

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