Question

There are officer and Assistant in an office. If 15 As- sistant went on leave then every Assistant has two officers, after that 45 officers went on leave now every officer has 5 Assistants. Then find out how many Assistant were there initially.

Answer 1

Answer:

Initially there were 40 Assistants.

Step-by-step explanation:

Let the number of of Assistants initially in the office be y and that of the officers be x.

If 15 assistants go on leave then the remaining assistants = y - 15

Each assistant will have 2 officers.

This is expressed as :

x/(y - 15) = 2

x = 2(y - 15)

x = 2y - 30

x - 2y = - 30

Divide through by - 1:

2y - x = 30…………i)

If 45 officers go on leave then we have :

Remaining officers = x - 45

Each officer will now have 5 Assistants:

We express this as :

(y - 15) / (x - 45) = 5

y - 15 = 5(x - 45)

y - 15 = 5x - 225

y - 5x = - 225 + 15

y - 5x = - 210

Divide through by - 1

5x - y = 210.......………ii)

We solve i and ii simultaneously :

2y - x = 30

5x - y = 210

Multiply equation ii by 2 then add the equations.

2y - x = 30

10x - 2y = 420

9x = 450

x = 450/9

x = 50

We substitute this in i to get y :

2y - 50 = 30

2y = 30 + 50

2y = 80

y = 80/2

y = 40

Initially there were 40 Assistants and 50 officers.