Question

The mean monthly salary paid to 300 employees of a firm is Rs. 1470. There are 200

male employees and the remaining are females. If the mean salary of females is Rs

1400,obtain the mean salary of males.

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Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Mean monthly salary paid to 300 employees of a firm is Rs. 1470}$

$\textsf{Number of male employees is 200}$

$\textsf{Mean salary of females is Rs.1400}$

$\underline{\textsf{To find:}}$

$\textsf{Mean salary of males}$

$\underline{\textsf{Solution:}}$

$\textsf{Combined mean formula:}$

$\boxed{\textsf{Combined mean}\mathsf{=\dfrac{n_1\,\bar{x_1}+n_2\,\bar{x_2}}{n_1+n_2}}}$

$\textsf{Here,}$

$\mathsf{n_1=200,\;n_2=100,\;\bar{x_2}=1400}$

$\implies\mathsf{1470=\dfrac{200\,\bar{x_1}+100(1400)}{300}}$

$\implies\mathsf{1470{\times}300=200\,\bar{x_1}+140000}$

$\implies\mathsf{441000=200\,\bar{x_1}+140000}$

$\implies\mathsf{441000-140000=200\,\bar{x_1}}$

$\implies\mathsf{200\,\bar{x_1}=301000}$

$\implies\mathsf{\bar{x_1}=\dfrac{301000}{200}}$

$\implies\boxed{\mathsf{\bar{x_1}=1505}}$

$\underline{\textsf{Answer:}}$

$\textsf{Mean salary of males is Rs.1505}$