Question

The average of monthly salary of 75 workers in a company
is = RS.6,000. If the manager's salary is added, the average
salary inserases by Rs.750 per month , what is the manager's monthly salary?​

Answer 1

Given :

• Number of worker = 75
• Average of monthly salary of 75 worker = Rs 6,000
• Increase in average of monthly salary when manager's salary is added = Rs 750

To find :

Manager's salary

Formula used :

Average = Sum of observation ÷ Number of observation

Solution :

Let ,

• Sum of monthly salary of 75 worker = x
• Monthly salary of manager = y

Case 1)

• Number of observation ( worker ) = 75
• Average of monthly salary of workers = Rs 6000
• Sum of monthly salary = x

Using Formula of average

$\sf \implies \: 6000 \: = \: \dfrac{x}{75} \:$

$\sf \implies \:x \: = \: 6000 \times 75$

$\sf \implies \:x \: = \:450000 \: \: \: \: \: \: \: \: \: \: equation \: 1$

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Case 2)

i) Number of observation ( workers + manager ) = 75+1

➝ Number of observation = 76

ii) Average of monthly salary ( workers + manager) = Average of monthly salary of workers + increase in average

➝ Average of monthly salary ( workers + manager) = Rs 6000 + Rs 750

➝ Average of monthly salary ( workers + manager) = Rs 6750

iii) Sum of observation = Sum of Monthly salary of workers + Monthly salary of manager

➝ Sum of observation = x + y

{ Put value of x from equation 1 into above equation }

➝ Sum of observation = 450000 + y

Using formula of average,

$\sf \implies \: 6750 \:=\: \dfrac{450000 + y}{76}$

$\sf \implies \: 450000 \: + \: y \:=\: 76 \times 6750$

$\sf \implies \: 450000 \: + \: y \:=\:513000$

$\sf \implies \: \: y \:=\:513000 \: - \: 450000 \:$

$\sf \implies \: y \: = \: 63000$

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ANSWER :

Monthly salary of Manager (y) = Rs 63,000