let

m = the number of male employees

M = the sum of the ages of all male employees

f = the number of female employees

F = the sum of the ages of all female employees

the average age of male employees in a firm is 52 years

M/m = 52 => M = 52m

the average age of female employees is 42 years

F/f = 42 => F = 42f

the mean age of all employees is 50 years

(F + M)/(f + m) = 50

F + M = 50(f + m)

lets plug M = 52m and F = 42f into the last equation

42f + 52m = 50(f + m)

42f + 52m = 50f + 50m

52m - 50m = 50f - 42f

2m = 8f divide both sides by 2

m = 4f

we need to find the percentage of male and female employees that is

m/(m + f) and f/(m + f)

if we plug m = 4f into the last equations we get

the percentage of male: 4f/(4f + f) = 4f/(5f) = 4/5 = 0.8 or 80%

the percentage of male of female: f/(4f + f) = f/(5f) = 1/5 = 0.2 or 20%

80% of the employees are male and the rest of the employees that is 20% are female.