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

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

If 15 assistants go on leave then the remaining assistants = X - 15.

Each assistant will have 2 officers :

$\\ {\sf~~~\implies~~~\dfrac{y}{x-15}= 2}$

${\sf~~~\implies~~~y= 2(x - 15)}$

${\sf~~~\implies~~~y= 2x - 30}$

${\sf~~~\implies~~~y - 2x= - 30}$

${\sf~~~\implies~~~2x - y= 30} \: \: \: \: \: \: - - - - - (1)$

If 45 officers go on leave then the remaining assistants = Y - 45

Each officer will now have 5 Assistants :

$\\ {\sf~~~\implies~~~\dfrac{x - 15}{y - 45}= 5}$

${\sf~~~\implies~~~x - 15= 5(y - 45)}$

${\sf~~~\implies~~~x - 15= 5y - 225}$

${\sf~~~\implies~~~x - 5y = - 225 + 15}$

${\sf~~~\implies~~~x - 5y = - 210}$

• Multiplying both sides by 2

${\sf~~~\implies~~~2x - 10y = - 420\: \: \: \: \: \: - - - - - (2)}$

Now, Subtracting 2 From 1

$\\ {\sf~~~\implies~~~2x - y - (2x - 10y)= 30 - ( - 420)}$

${\sf~~~\implies~~~2x - y - 2x + 10y= 30 + 420}$

${\sf~~~\implies~~~9y= 450}$

${\sf~~~\implies~~~y= 50}$

Putting the value of y in 1

${\sf~~~\implies~~~2x - 50= 30}$

${\sf~~~\implies~~~2x= 30 + 50}$

${\sf~~~\implies~~~2x= 80}$

${\sf~~~\implies~~~x= 40}$

$~~~~~~~~\sf{\therefore\underbrace{There ~~are ~~\bf40~~\sf many~~ Assistant ~~were~~ there ~~initially.}}$

Answer 2

Answer:

↪️ Initially there were 40 Assistants and 50 officers.

◆ For explanation see the attachment photos.

◆ Don't forget to thanks

◆ Mark as brainlist.