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 answer is 60.

Based on the provided pie chart titled "Percentage share of skills in 2010", the percentage distribution of the 600 total employees across the five skill levels is as follows:
• Skill level P: 20%
• Skill level Q: 25%
• Skill level R: 25%
• Skill level S: 25%
• Skill level T: 5%

First, we calculate the number of employees at each skill level in 2010:
• Number of employees at skill level P in 2010:
$600\times \frac{20}{100}=120$
• Number of employees at skill level Q in 2010:
$600\times \frac{25}{100}=150$
• Number of employees at skill level R in 2010:
$600\times \frac{25}{100}=150$
• Number of employees at skill level S in 2010:
$600\times \frac{25}{100}=150$
• Number of employees at skill level T in 2010:
$600\times \frac{5}{100}=30$

The total employment increased by 15% from 2010 to 2016. Therefore, the total number of employees in 2016 is:
$\text{Total employees in 2016}=600\times (1+0.15)=600\times 1.15=690$

According to the problem description:
• The total employment at skill levels P, Q, and R remained unchanged from 2010 to 2016. Thus, in 2016:
$\text{P (2016)}=120$
$\text{Q (2016)}=150$
$\text{R (2016)}=150$
• The employment at skill level S increased by 40% from 2010 to 2016. Thus, in 2016:
$\text{S (2016)}=150\times (1+0.40)=150\times 1.40=210$

We can now find the number of employees at skill level T in 2016 by subtracting the sum of employees at skill levels P, Q, R, and S from the total employment in 2016:
$\text{T (2016)}=\text{Total (2016)}-[\text{P (2016)}+\text{Q (2016)}+\text{R (2016)}+\text{S (2016)}]$
$\text{T (2016)}=690-[120+150+150+210]$
$\text{T (2016)}=690-630=60$

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