Question

the ratio of the number of employees in two verticals of a bank 10:11 .if 20 employees ARE ADDED to each of the verticals , then the ratio of the number of employees become 14:15 .find the initial number of employees in each vertical

Answer 1

Answer:

50 in first vertical

55 in second vertical

Answer 2

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 $\frac{x}{y}$ = $\frac{10}{11}$

=> 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,

$\frac{x+20}{y+20}$ = $\frac{14}{15}$

=> 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.