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.

Cities	Males in Private company	Males in Public company	Females (private + public)
A	15x – 2y	y	55
B	16x	16	108
C	9y	24	74
D	84	21	85

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.

The correct answer is City A and City B.

Step-by-step Explanation:

Step 1: Calculate the values of x and y from the given notes.

From Note (i), the total number of male employees in City A is 50. Total males in City A is the sum of males in private and public companies:

$(15x-2y)+y=50$

$15x-y=50$     --- (Equation 1)

From Note (ii), the total males working in private companies from B and C is 154:

$16x+9y=154$     --- (Equation 2)

From Equation 1, we get $y=15x-50$. Substituting this value of y into Equation 2:

$16x+9(15x-50)=154$

$16x+135x-450=154$

$151x=604$

$x=4$

Now, solve for y:

$y=15\left(4\right)-50=60-50=10$

Step 2: Find the number of males in private companies for each city.

• City A: $15x-2y=15\left(4\right)-2\left(10\right)=60-20=40$

• City B: $16x=16\left(4\right)=64$

• City C: $9y=9\left(10\right)=90$

• City D: 84 (given directly in the table)

Step 3: Calculate the average number of males working in private companies across all 4 cities.

$\text{Total males in private companies}=40+64+90+84=278$

$\text{Average}=\frac{278}{4}=69.5$

Step 4: Identify cities where males working in private companies is less than the average (69.5).

• City A = 40 (less than 69.5)

• City B = 64 (less than 69.5)

• City C = 90 (greater than 69.5)

• City D = 84 (greater than 69.5)

Therefore, the cities where males working in a private company is less than the average are City A and City B.