Line graph shows number of departments and average number of employees in all the departments in five different companies (P, Q, R, S and T). Read the following line graph carefully and answer the questions given below.

Number of departments in company U is 40% more than that of in company R and the ratio of total number of employees in all the departments of company P to that of in company U is 3 : 2. Find the average number of employees in all the department of company U.

The correct answer option is 25.

Step 1: Extract values from the line graph for Company P and Company R

From the line graph provided in the question:

• For Company P:
- Number of departments (blue line) = 15
- Average number of employees in all departments (orange line) = 35

• For Company R:
- Number of departments (blue line) = 10
- Average number of employees in all departments (orange line) = 40

Step 2: Calculate the total number of employees in Company P

Total number of employees in Company P = (Number of departments in P) × (Average number of employees per department in P)

$\text{Total employees in P}=15\times 35=525$

Step 3: Calculate the number of departments in Company U

It is given that the number of departments in Company U is 40% more than that of Company R.

$\text{Number of departments in U}=10+\left(40\%\text{of}10\right)$

$\text{Number of departments in U}=10+4=14$

Step 4: Calculate the total number of employees in Company U

The ratio of total number of employees in Company P to Company U is given as 3 : 2.

$\frac{\text{Total employees in P}}{\text{Total employees in U}}=\frac{3}{2}$

$\frac{525}{\text{Total employees in U}}=\frac{3}{2}$

$\text{Total employees in U}=\frac{525\times 2}{3}=175\times 2=350$

Step 5: Find the average number of employees in all departments of Company U

$\text{Average number of employees in U}=\frac{\text{Total number of employees in U}}{\text{Number of departments in U}}$

$\text{Average number of employees in U}=\frac{350}{14}=25$

Hence, the average number of employees in all the departments of company U is 25.