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JEE Main 20178 AprilOnline
Exam
JEE Main
Year
2017
Date
8 April
Mode
Online
Subject
Mathematics
Chapter
Statistics

JEE Main 2017 · 8 April · Online · Mathematics · Statistics

The mean age of 25 teachers in a school is 40 years. A teacher...

The mean age of 2525 teachers in a school is 4040 years. A teacher retires at the age of 6060 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 3939 years, then the age (in years) of the newly appointed teacher is

Options

  1. A3535
  2. B4040
  3. C2525
  4. D3030

Correct answer

A. 3535

Step-by-step solution

Mean age can be calculated as

x−=x1+x2+…x2525=40\overset{-}{x} = \dfrac{{x}_{1} + {x}_{2} + \ldots {x}_{25}}{25} = 40

⇒⇒ x1+x2+…+x25=1000{x}_{1} + {x}_{2} + \ldots + {x}_{25} = 1000

Let age of new teacher be A, then

1000−60+A=39×25=9751000 - 60 + A = 39 \times 25 = 975

⇒⇒ A=975−940=35A = 975 - 940 = 35
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