The following table shows the percentage (%) distribution of number of…
2022
The following table shows the percentage (%) distribution of number of students qualifying an Entrance Exam from seven schools A-G in the years 2020 and 2021. The number of students qualifying from School G in 2020 and 2021 are 90 and 135, respectively. Based on the data in the table, answer the questions 1-5:
School | Distribution (%) of Qualified students | |
|---|---|---|
2020 | 2021 | |
A | 21% | 23% |
B | 14% | 8% |
C | 16% | 11% |
D | 10% | 14% |
E | 18% | 16% |
F | 9% | 13% |
G | 12% | 15% |
The ratio of the number of students qualifying from Schools B, C and D in 2020 to that of Schools E, F and G in 2021 is
Answer: D. 25:33 — ConceptWhen a subgroup percentage and its actual count are known, the total for that year is actual count divided by the percentage expressed as a decimal.…
- A.
2:3
- B.
51:75
- C.
3:2
- D.
25:33
Attempted by 1 students.
Show answer & explanation
Correct answer: D
Concept
When a subgroup percentage and its actual count are known, the total for that year is actual count divided by the percentage expressed as a decimal. Percentages from different years must first be converted into actual counts because the yearly totals may differ.
Application
For 2020, School G represents 12% and has 90 qualified students, so the 2020 total is 90 ÷ 0.12 = 750.
Schools B, C and D together represent 14% + 16% + 10% = 40% in 2020; their count is 0.40 × 750 = 300.
For 2021, School G represents 15% and has 135 qualified students, so the 2021 total is 135 ÷ 0.15 = 900.
Schools E, F and G together represent 16% + 13% + 15% = 44% in 2021; their count is 0.44 × 900 = 396.
Therefore, the required ratio is 300:396. Dividing both terms by 12 gives 25:33.
Cross-check
25 × 396 = 9,900 and 33 × 300 = 9,900, so the simplified ratio preserves the two computed totals.