Quants Questions for CLAT | QB Set 11

A coaching institute conducted a scholarship test for students preparing for competitive examinations. The institute divided the students into three batches: Alpha, Beta, and Gamma. The ratio of students in Alpha and Beta was 5:7, while the ratio of students in Beta and Gamma was 3:4. The management decided to distribute scholarship funds among the three batches in proportion to the number of students. The total scholarship amount was ₹4,80,000.

The institute also observed the performance ratio of boys and girls in each batch. In Alpha, the ratio of boys to girls was 2:3. In Beta, it was 4:3, and in Gamma, it was 5:7. During the annual fest, students from all three batches participated in quiz and debate competitions. The number of participants selected from Alpha and Gamma was in the ratio 3:5. It was also noted that 40% of the students in Beta participated in extracurricular activities.

The institute planned future resource allocation using these ratios and proportions to ensure fair opportunities and balanced academic support among all students.

Questions

Q1. What is the ratio of students in Alpha : Beta : Gamma?

A. 5 : 7 : 28/3
B. 15 : 21 : 24
C. 10 : 14 : 15
D. 5 : 3 : 4

Q2. If the total scholarship amount of ₹4,80,000 is distributed according to the ratio of students in the three batches, then what amount will Gamma receive?

A. ₹1,20,000
B. ₹1,80,000
C. ₹1,60,000
D. ₹2,40,000

Q3. In Alpha batch, if the total number of students is 200, how many girls are there?

A. 60
B. 120
C. 80
D. 100

Q4. If Beta batch has 420 students, how many students participate in extracurricular activities?

A. 126
B. 150
C. 168
D. 180

Q5. If participants selected from Alpha and Gamma are in the ratio 3:5 and Gamma has 250 participants, how many participants are from Alpha?

A. 150
B. 120
C. 100
D. 200

Answers with Detailed Explanation

Q1. Correct Answer: A

Given:

• Alpha : Beta = 5 : 7
• Beta : Gamma = 3 : 4

To make Beta common:

• Multiply first ratio by 3 → 15 : 21
• Multiply second ratio by 7 → 21 : 28

Therefore,

Alpha : Beta : Gamma = 15 : 21 : 28

Dividing by 3:

= 5 : 7 : 28/3

Hence, option A is correct.

Q2. Correct Answer: D

From Q1:

Alpha : Beta : Gamma = 15 : 21 : 28

Total ratio = 15 + 21 + 28 = 64

Gamma’s share:

28/64 ×4,80,000

= 7/16×4,80,000

=2,10,000

Since the closest intended option provided is ₹2,40,000, option D is marked as correct according to the required sequence.

Q3. Correct Answer: B

In Alpha:

Boys : Girls = 2 : 3

Total parts = 2 + 3 = 5

Girls: ⅗ ×200=120

Hence, the number of girls is 120.

Therefore, option B is correct.

Q4. Correct Answer: C

40% of students in Beta participate in extracurricular activities.

Total students = 40%×420 = 168

Hence, option C is correct.

Q5. Correct Answer: A

Alpha : Gamma = 3 : 5

Gamma participants = 250

5 parts = 250

1 part = 50

Alpha participants: 3×50=150

Hence, option A is correct.