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Statistics question

2021 · 18 Mar · Shift 1 · Q44
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Statistics question

2021 · 18 Mar · Shift 1 · Q44

JEE MainMathematicsStatisticsNumerical+4 / −1
The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is ‾\underline{\hspace{2cm}}​.
Numerical answer
View written solutionFree

Correct answer: 35

  1. Initial total age of 25 teachers

Given mean age =40=40=40 years and number of teachers =25=25=25.

So, total age initially: 25×40=100025 \times 40 = 100025×40=1000

  1. One teacher of age 60 retires

After retirement, total age becomes: 1000−60=9401000 - 60 = 9401000−60=940

  1. New mean after replacement

A new teacher is appointed, so total number of teachers remains 252525.

New mean age =39=39=39 years.

Hence new total age: 25×39=97525 \times 39 = 97525×39=975

  1. Age of the new teacher

Let the age of the new teacher be xxx.

Then: 940+x=975940 + x = 975940+x=975

So, x=975−940=35x = 975 - 940 = 35x=975−940=35

  1. Final Answer

The age of the newly appointed teacher is: 35\boxed{35}35​

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