A firm hires employees at five different skill levels P, Q, R, S, T. The shares of employment at these skill levels of total employment in 2010 is given in the pie chart as shown. There were a total of 600 employees in 2010 and the total employment increased by 15% from 2010 to 2016. The total employment at skill levels P, Q and R remained unchanged during this period. If the employment at skill level S increased by 40% from 2010 to 2016, how many employees were there at skill level T in 2016?

The correct option is 60.

Step-by-Step Explanation:

Step 1: Analyze the data from the pie chart for the year 2010
From the provided pie chart titled "Percentage share of skills in 2010", we can extract the percentage share of each skill level of the total employment:
• Skill level P = 20%
• Skill level Q = 25%
• Skill level R = 25%
• Skill level S = 25%
• Skill level T = 5%

The total number of employees in 2010 was 600. Using these percentages, we can calculate the number of employees at each skill level in 2010:

• Number of employees at skill level P in 2010:
$20\%\text{\hspace{0.5em}of\hspace{0.5em}}600=\frac{20}{100}\times 600=120$

• Number of employees at skill levels Q, R, and S in 2010 (each has a 25% share):
$25\%\text{\hspace{0.5em}of\hspace{0.5em}}600=\frac{25}{100}\times 600=150$
So, there were 150 employees each at skill levels Q, R, and S.

Step 2: Calculate the total employment in 2016
We are given that the total employment increased by 15% from 2010 to 2016.

Total employees in 2016:
$600\times \left(1+0.15\right)=600\times 1.15=690$

Step 3: Account for employment changes at skill levels P, Q, R, and S
• The total employment at skill levels P, Q, and R remained unchanged during this period:
P₂₀₁₆ + Q₂₀₁₆ + R₂₀₁₆ = P₂₀₁₀ + Q₂₀₁₀ + R₂₀₁₀ = 120 + 150 + 150 = 420 employees.

• The employment at skill level S increased by 40% from 2010 to 2016:

Number of employees at skill level S in 2016:
$150\times \left(1+0.40\right)=150\times 1.40=210$

Step 4: Find the number of employees at skill level T in 2016
The total employment in 2016 is the sum of the employment at all five levels (P, Q, R, S, T):

$\text{Total\hspace{0.5em}Employment\hspace{0.5em}}\left(2016\right)=\left(P_{2016}+Q_{2016}+R_{2016}\right)+S_{2016}+T_{2016}$
Substitute the calculated values into the equation:
$690=420+210+T_{2016}$
$690=630+T_{2016}$
$T_{2016}=690-630=60$

Therefore, there were 60 employees at skill level T in 2016.