Question

The mean salary of 20 workers is Rs.10.250. If the salary of office superintendent
bied, the mean will increase by Rs.750. Find the salary of the office superintende​

Answer 1

Question :-

The mean salary of 20 workers is Rs.10,250. If the salary of office superintendent bied, the mean will increase by Rs.750. Find the salary of the office superintende .

Answer :-

Salary of office superintendent is ₹26,000

To Find :-

→ Salary of the office supernitende .

Solution :-

Given that :

• Mean salary =₹ 10,250

• Total number of workers = 20

• mean increased =₹ 750

Now ,

we know that ,

$\to \sf \: mean \: \frac{sum \: of \: observations}{number \: of \: observations} \\ \\ \to \sf sum \: of \: obs. = mean \times no. \: of \: obs. \\ \\ \to \sf \: sum \: of \: observations = 10250 \times 20 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 205000$

now ,salary of office superintendent is added hence ,

• Number of observations = 21

• Let, the salary of office superintendent is "y" .

now, according to the question,

→ salary increased by ₹750 ,

hence ,

$\to \sf 10250 + 750 = \frac{sum \: of \: observations}{21} \\ \\ \to \sf 11000 = \frac{205000 + y}{21} \\ \\ \to \sf \: y + 205000 = 21 \times 11000 \\ \\ \to \sf y = 231000 - 205000 \\ \\ \to \boxed{\sf \: y =2 6000}$

hence ,salary of office superintendent is ₹26,000

Answer 2

Answer:

$\small\bold\red{Salary \: }$ = $\huge{\boxed{\mathfrak\green{Rs.26,000}}}$

Step-by-step explanation:

Let salary of office superintendent be X

Given:-

• Mean salary of 20 workers = Rs.10,250
• If salary of office superintendent is added, mean will increase by Rs.750

• Salary of superintendent = ?

${\boxed{\bold{Mean =\dfrac{Sum\:of\:salaries}{Number\:of\:workers} }}}$

$\Rightarrow\sf 10250 =\dfrac{Sum\:of\:salaries}{20} \\\\\Rightarrow\sf Sum\:of\:salaries = 10250 \times 20 \\\\\Rightarrow{\boxed{\bold\red{Sum\:of\:salaries = Rs.205,000 }}}$

$\rule{300}{1}$

Now according to question :-

• Number of workers = 21
• Mean increases = Rs.750
• Salary of the office superintendent=?

$\Rightarrow\sf (10250 + 750)<strong> </strong>= \dfrac{205,000 + X }{21} \\\\\Rightarrow\sf 11,000 =\dfrac{205,000 + X}{21} \\\\\Rightarrow\sf 205,000 + X = 11,000 \times 21 \\\\\Rightarrow\sf 205,000 + X = 231,000 \\\\\Rightarrow\sf X = Rs.(231,000 - 205,000) \\\\\Rightarrow\huge{\boxed{\mathfrak\green{X = Rs.26,000 }}}$

$\therefore\bold{\underline{Salary\:of\:office\:superintendent = Rs.26,000 }}$