Percentages Question 1 - CAT 2024
In a group of 250 students, the percentage of girls was at least 44% and at most 60%. The remaining students were boys. Each student opted for either swimming or running or both.
- 50% of the boys and 80% of the girls opted for swimming.
- 70% of the boys and 60% of the girls opted for running.
The minimum and maximum possible number of students who opted for both swimming and running, respectively, are:
Step-by-Step Explanation
Let the number of girls be G. Since there are 250 students,
110 ≤ G ≤ 150
The total number of swimming enrolments is:
0.5B + 0.8G
The total number of running enrolments is:
0.7B + 0.6G
Using the overlap formula,
Both = (Swimming + Running) − Total Students
This simplifies to:
Both = 0.2(250 + G)
Minimum value occurs when G = 110:
0.2(250 + 110) = 72
Maximum value occurs when G = 150:
0.2(250 + 150) = 80
Hence, the minimum and maximum possible numbers are 72 and 80, respectively.
💡 FundaMakers Tip: Whenever students choose either one or both activities, use the overlapping (inclusion-exclusion) principle. It saves a lot of time.