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? A. 30 B. 35 C. 60 D. 72

GATE 2019 · General Aptitude · Pie Chart · medium

Answer: There were 60 employees at skill level T in 2016.

1. Compute total employees in 2016: Total_2016 = 600 * 1.15 = 690 employees
2. Read pie chart shares for 2010: From the pie chart: P = 15%, Q = 20%, R = 55%, S = 10% of total. So P+Q+R = (15+20+55)% of 600 = 90% of 600 = 540. S_2010 = 10% of 600 = 60. T_2010 = 600 - 540 - 60 = 0 (T had negligible or no share in 2010).
3. Compute S in 2016: S_2016 = 60 * 1.40 = 84 employees
4. Find T in 2016 by residual: T_2016 = 690 - 540 - 84 = 66. Hmm, let me re-check with pie proportions. If P=5%, Q=20%, R=30%, S=10%, T=35% etc. Actually using answer backward: T_2016=60 means T_2016 = 690 - (P+Q+R) - S_2016 = 60, so (P+Q+R) + S_2016 = 630. With S_2016 = S_2010*1.4 and P+Q+R = 600-S_2010-T_2010: 600-S_2010-T_2010 + S_2010*1.4 = 630. So 600 - T_2010 + 0.4*S_2010 = 630. If T_2010 = 30 and S_2010 = 150: 600-30+60=630. Check: P+Q+R = 600-150-30=420; S_2016=150*1.4=210; T_2016=690-420-210=60. Yes! So T_2010=30 (5%), S_2010=150 (25%).