**Read carefully the information and answer the question that follows.**

A college received fifty applications for a certain course. In the qualifying examination, one-tenth of them secured marks in the 90-95% range. Within remaining segment, three-fifths of them secured marks in 75-90% range. The rest secured below 75%. To get admission, the following restrictions hold good

i. No student who has scored below 75% can seek admission to Physics course.

ii. No student is allowed to opt Physics without opting Mathematics.

iii. No student is allowed to opt Physics and Astrophysics simultaneously.

iv. To opt Mathematics or Astrophysics, a student should have scored at least 70% in the qualifying examination.

**Which one of the following alternatives is possible?**

#### Options

Ninety percent of the applicants are admitted to Physics course.

Thirty-five percent of the applicants who are otherwise ineligible to join Physics course are admitted to Mathematics and Astrophysics course

Students of Physics course outnumber those of Mathematics.

Whoever is eligible to study Mathematics is also eligible to study Physics.

#### Solution

**Thirty-five percent of the applicants who are otherwise ineligible to join Physics course are admitted to Mathematics and Astrophysics course**

**Explanation:**

'Thirty-five percent of the applicants who are otherwise ineligible to join Physics course are admitted to Mathematics and Astrophysics course.' is the only possible option. If 35% of those who scored below 75% scored between 75% and 70%, then they can opt for Mathematics and Astrophysics.