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JEE Main 201510 AprilOnline
Exam
JEE Main
Year
2015
Date
10 April
Mode
Online
Subject
Mathematics
Chapter
Statistics

JEE Main 2015 · 10 April · Online · Mathematics · Statistics

A factory is operating in two shifts, day and night, with 70 and 30...

A factory is operating in two shifts, day and night, with 7070 and 3030 workers, respectively.If per day mean wage of the day shift workers is, ₹54₹ 54 and per day mean wage of all the workers is ₹60₹ 60, then per day mean wage of the night shift workers (in ₹₹) is :

Options

  1. A7575
  2. B7474
  3. C6969
  4. D6666

Correct answer

B. 7474

Step-by-step solution

n1x¯1+n2x¯2n1+n2=x¯\dfrac{{n}_{1}{\overset{¯}{x}}_{1} + {n}_{2}{\overset{¯}{x}}_{2}}{{n}_{1} + {n}_{2}} = \overset{¯}{x}

70⋅(54)+30(x¯2)70+30=60\dfrac{70 ⋅ \left(54\right) + 30\left({\overset{¯}{x}}_{2}\right)}{70 + 30} = 60

⇒3780+30x¯2=6000⇒ 3780 + 30\overset{¯}{x}2 = 6000

∴x¯2=6000−378030∴ {\overset{¯}{x}}_{2} = \dfrac{6000 - 3780}{30}

=222030= \dfrac{2220}{30}

=74= 74
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