A company has three types of employees: A, B, and C. Among the total pool of employees, A:B:C = 3:4:6 in 2009. Between 2009 and 2010, both A & B increased by 50%, and C doubled. What fraction of the employees were C by 2010?
Double the entire ratio, so that 50% increases are easier.
3:4:6 = 6:8:12
An increase of 50% is an increase by half the amount, so 6 increases by 3 to 9, and 8 increased by 4 to 12. Those are the first two. C doubles, from 12 to 24. The 2010 ratio is
9:12:24 = 3:4:8
Of the 3 + 4 + 8 = 15 parts, 8 parts are C, so C accounts for 8/15 of the employees in 2010.