The following table shows the percentage (%) distribution of total number of…
2022
The following table shows the percentage (%) distribution of total number of students and total number of girls studying in six colleges A-F. Total number of students and girls studying in all the colleges together are 60000 and 24000 respectively. Based on the data in the table, answer the questions 1-5:
College-wise Distribution of Students
College | Students (out of 60000) | Girls (out of 24000) |
|---|---|---|
A | 10% | 15% |
B | 9% | 12% |
C | 23% | 18% |
D | 18% | 14% |
E | 16% | 20% |
F | 24% | 21% |
The ratio of the number of boys in College F with the number of boys in College D is
Answer: B. 39 : 31 — CONCEPTWhen a category total and a subgroup total are distributed by percentages, calculate each count from its own grand total. The complementary count…
- A.
31 : 39
- B.
39 : 31
- C.
29 : 37
- D.
37 : 29
Attempted by 3 students.
Show answer & explanation
Correct answer: B
CONCEPT
When a category total and a subgroup total are distributed by percentages, calculate each count from its own grand total. The complementary count equals the category total minus the subgroup count. Form the requested ratio in the stated order and simplify both terms by their greatest common divisor.
APPLICATION
College F has 24% of 60,000 students: (24/100) × 60,000 = 14,400.
College F has 21% of 24,000 girls: (21/100) × 24,000 = 5,040.
Therefore, boys in College F = 14,400 − 5,040 = 9,360.
College D has 18% of 60,000 students: (18/100) × 60,000 = 10,800.
College D has 14% of 24,000 girls: (14/100) × 24,000 = 3,360.
Therefore, boys in College D = 10,800 − 3,360 = 7,440.
The requested ratio is F : D = 9,360 : 7,440. Dividing both terms by 240 gives 39 : 31.
College | Students | Girls | Boys |
|---|---|---|---|
F | 14,400 | 5,040 | 9,360 |
D | 10,800 | 3,360 | 7,440 |
CROSS-CHECK
Multiplying the simplified terms by 240 returns 39 × 240 = 9,360 and 31 × 240 = 7,440, so the simplification preserves both computed counts.
Hence, the ratio of boys in College F to boys in College D is 39 : 31.