CAT 2022 Set-3 | Data Interpretation and Logical Reasoning | Question: 12

Question

Comprehension:
All the first-year students in the computer science (CS) department in a university take both the courses (i) $\mathrm{Al}$ and (ii) $\mathrm{ML}$. Students from other departments (non-CS students) can also take one of these two courses, but not both. Students who fail in a course get an $\mathrm{F}$ grade; others pass and are awarded $\mathrm{A}$ or $\mathrm{B}$ or $\mathrm{C}$ grades depending on their performance. The following are some additional facts about the number of students who took these two courses this year and the grades they obtained.

1. The numbers of non-CS students who took $\mathrm{Al}$ and $\mathrm{ML}$ were in the ratio $2: 5$.
2. The number of non-CS students who took either $\mathrm{Al}$ or $\mathrm{ML}$ was equal to the number of CS students.
3. The numbers of non-CS students who failed in the two courses were the same and their total is equal to the number of CS students who got a $\mathrm{C}$ grade in $\mathrm{ML}$.
4. In both the courses, $50 \%$ of the students who passed got a $\mathrm{B}$ grade. But, while the numbers of students who got $\mathrm{A}$ and $\mathrm{C}$ grades were the same for $\mathrm{Al}$, they were in the ratio $3 : 2$ for $\mathrm{ML}$.
5. No CS student failed in $\mathrm{Al}$, while no non-CS student got an $\mathrm{A}$ grade in $\mathrm{Al}$.
6. The numbers of CS students who got $\mathrm{A, B}$ and $\mathrm{C}$ grades respectively in $\mathrm{Al}$ were in the ratio $3: 5: 2$, while in $\mathrm{ML}$ the ratio was $4: 5: 2$.
7. The ratio of the total number of non-CS students failing in one of the two courses to the number of CS students failing in one of the two courses was $3: 1$.
8. $30$ students failed in $\mathrm{ML}$.

How many CS students failed in $\mathrm{ML}$?