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Q)

The average salary of male employees in a factory was Rs. 520 and that of females was Rs. 420. If mean salary of all employees is Rs. 500, the % of male employees is?

$\begin {array} {1 1} (A)\;20 & \quad (B)\;40 \\ (C)\;60 & \quad (D)\;80 \end {array}$

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A)
• $\overline x = \large\frac{n_1\overline x _1+n_2\overline x _2}{n_1+n_2}$
$\overline x = \large\frac{n_1\overline x _1+n_2\overline x _2}{n_1+n_2}$
$500 = \large\frac{n_1(520)+n_2(420)}{n_1+n_2}$
$500 (n_1+n_2)=520n_1+420n_2$
$500n_1+500n_2=520n_1+420n_2$
$500n_1-520n_1=420n_2-500n_2$
$-20n_1=-80n_2$
$\large\frac{n_1}{n_2} = \large\frac{\not{-}8\not{0}}{\not{-}2\not{0}}$
$\large\frac{n_1}{n_2}=\large\frac{4}{1}$
$\therefore$ percentage of male employees = 80