Question

The average salary of 150 workers is Rs. 75 per week . Out of these 150 workers 60 are female with average salary equal to Rs. 70 per week .Find out Average salary of male workers.

Answer 1

$\textbf{Given:}$

$\textsf{Average salary of 150 workers is Rs.75}$

$\textsf{Number of female workers is 60 and their average}$

$\textsf{salary per week is Rs.70}$

$\textbf{To find:}$

$\textsf{Find the average salary of male workers}$

$\textbf{Solution:}$

$\mathsf{No.of\;female\;workers,\;n_1=60}$

$\mathsf{No.of\;male\;workers,\;n_2=90}$

$\mathsf{Here,\;average\;salary\;of\;150\;workers\;\overline{x}=75,\;}$

$\mathsf{Average\;salary\;of\;female\;workers\;\overline{x_1}=70,\;}$

$\mathsf{Let\;the\;average\;salary\;of\;male\;workers\;be\;\overline{x_2}}$

$\textsf{Using combined mean formula,}$

$\boxed{\mathsf{\overline{x}=\dfrac{n_1\,\overline{x_1}+n_2\,\overline{x_2}}{n_1+n_2}}}$

$\implies\mathsf{75=\dfrac{60{\times}70+90{\times}\overline{x_2}}{60+90}}$

$\implies\mathsf{75=\dfrac{4200+90{\times}\overline{x_2}}{150}}$

$\implies\mathsf{11250=4200+90{\times}\overline{x_2}}$

$\implies\mathsf{7050=90{\times}\overline{x_2}}$

$\implies\mathsf{\overline{x_2}=\dfrac{7050}{90}}$

$\implies\mathsf{\overline{x_2}=Rs.\,78.33}$

$\textbf{Answer:}$

$\textsf{Average salary of male workers per week is Rs.78.33}$

Answer 2

Given : The average salary of 150 workers is Rs. 75 per week .  60 are female with average salary equal to Rs. 70 per week .

To Find : Average salary of male workers.

Solution:

The average salary of 150 workers is Rs. 75 per week .

=> Total Salary per week = 150 x 75

= 11250

60 are female with average salary equal to Rs. 70 per week .

=> Total Salary of Females per week  = 60 x 70

= 4200

Total Salary of Males  per week = 11250  - 4200

= 7050

Males = 150 - 60 = 90

Average salary of male workers per week   = 7050/90

= 705/9

= 235/3

= 78.33

Average salary of male workers  = 78.33 Rs

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