Read the information and answer the following questions. The table shows the…
2023
Read the information and answer the following questions.
The table shows the number of males working in private and public companies and number of females working in private and public company in four (A, B, C & D) different cities.
Note –
(i) Number of male employees in A are 50.
(ii) Total males working in private company from B and C are 154.
(iii) Total employees (male + female) working in any city = private companies + public company (iv) Males/females working in any city = Sum of males/females working in private and public company.
In which of the following cities, males working in private company is less than the average number of males working in private company.
- A.
City C
- B.
City B
- C.
City A
- D.
City A and City B
- E.
City B and City C
Attempted by 1 students.
Show answer & explanation
Correct answer: D
Concept: Two algebraic conditions in two unknowns give a unique solution. Form one linear equation from each given note, solve the pair simultaneously, substitute back to get every cell's value, then the average of a set of values is their sum divided by the count; a value is "below average" when it is strictly less than that mean.
Setting up the equations from the table:
Note (i): total males in A = private + public = (15x − 2y) + y = 15x − y = 50.
Note (ii): private males in B + private males in C = 16x + 9y = 154.
Solving the two equations:
From 15x − y = 50, write y = 15x − 50.
Substitute into 16x + 9y = 154: 16x + 9(15x − 50) = 154.
Expand: 16x + 135x − 450 = 154, so 151x = 604, giving x = 4.
Then y = 15(4) − 50 = 60 − 50 = 10.
Private-company male counts (substituting x = 4, y = 10):
City | Expression | Private males |
|---|---|---|
A | 15x − 2y = 60 − 20 | 40 |
B | 16x = 16 × 4 | 64 |
C | 9y = 9 × 10 | 90 |
D | given | 84 |
Average and comparison:
Sum of private males = 40 + 64 + 90 + 84 = 278.
Average = 278 ÷ 4 = 69.5.
Compare each city with 69.5: A = 40 (below), B = 64 (below), C = 90 (above), D = 84 (above).
Result: The cities whose private-company male count is below the average of 69.5 are City A (40) and City B (64).
Cross-check: Verify the solved values against the notes — males in A = 40 + 10 = 50 (matches Note i), and private males in B + C = 64 + 90 = 154 (matches Note ii), so x = 4 and y = 10 are confirmed.