Answer:
Initially, there were 50 employees in 1 vertical and 55 in another vertical.
Step-by-step explanation:
Let there be 'x' employee in one vertical and 'y' in another vertical.
It is given that [tex]\frac{x}{y}[/tex] = [tex]\frac{10}{11}[/tex]
=> 11x = 10y
=> 11x - 10y = 0 --(i)
Now, 20 employees are added in each vertical.
Therefore, the new number of employees in 1st vertical = x + 20
and the new number of employees in 2nd vertical = y + 20
Now, the ratio becomes,
[tex]\frac{x+20}{y+20}[/tex] = [tex]\frac{14}{15}[/tex]
=> 15 (x + 20) = 14 (y + 20)
=> 15x + 300 = 14y + 280
=> 15x - 14y = 280 - 300
=> 15x - 14y = -20 --(ii)
Multiplying equation (i) by 14 and equation (ii) by 10
=> 154x - 140y = 0
150x - 140y = -200
=> 4x = 200
=> x = 50
Substituting x = 50 in equation (i), we have,
11*50 - 10y = 0
=> 550 = 10y
=> y = 55
Therefore, initially, there were 50 employees in 1 vertical and 55 in another vertical.