The following table presents the details about the percentage (%) distribution…
2022
The following table presents the details about the percentage (%) distribution of teachers and the number of male teachers in six different cities (A-F). There is a total of 4500 teachers in all the six cities together. Based on the data in the table, answer the questions 1-5:
City-wise Distribution of Teachers
City | Percentage of Teachers (%) | Number of Male Teachers |
|---|---|---|
A | 14% | 200 |
B | 16% | 400 |
C | 28% | 600 |
D | 15% | 100 |
E | 21% | 500 |
F | 06% | 100 |
In which city or cities is the number of male teachers greater than the number of female teachers?
Answer: C. Both B and E — ConceptA percentage share converts to a count by multiplying the total by the percentage and dividing by 100. When one subgroup count is known, the…
- A.
B only
- B.
D only
- C.
Both B and E
- D.
Both E and F
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept
A percentage share converts to a count by multiplying the total by the percentage and dividing by 100.
When one subgroup count is known, the complementary subgroup equals the group total minus the known subgroup. Male teachers outnumber female teachers exactly when the male count exceeds half of the city total.
Application
Convert each percentage into a city total: A = 4500 × 14/100 = 630; B = 4500 × 16/100 = 720; C = 4500 × 28/100 = 1260; D = 4500 × 15/100 = 675; E = 4500 × 21/100 = 945; F = 4500 × 6/100 = 270.
Subtract the male count from each city total to obtain female teachers: A = 630 − 200 = 430; B = 720 − 400 = 320; C = 1260 − 600 = 660; D = 675 − 100 = 575; E = 945 − 500 = 445; F = 270 − 100 = 170.
Compare the two counts city by city: 400 > 320 for B and 500 > 445 for E; in A, C, D, and F, the male count is smaller than the female count.
Cross-check
The half-total test gives the same conclusion: B has 400 males against half of 720, which is 360; E has 500 males against half of 945, which is 472.5. Every other city has a male count below half of its total.
City | Total teachers | Male teachers | Half of total | Male count vs half |
|---|---|---|---|---|
A | 630 | 200 | 315 | Below |
B | 720 | 400 | 360 | Above |
C | 1260 | 600 | 630 | Below |
D | 675 | 100 | 337.5 | Below |
E | 945 | 500 | 472.5 | Above |
F | 270 | 100 | 135 | Below |
Therefore, the cities are B and E.