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Statistics question

2017 · 8 Apr · Shift 1 · Q39
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Statistics question

2017 · 8 Apr · Shift 1 · Q39

JEE MainMathematicsStatisticsMCQ+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 now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly appointed teacher is :
  1. A
    25
  2. B
    30
  3. C
    35
  4. D
    40
View written solutionFree

Correct answer: C

  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 aged 60 retires

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

  1. New mean becomes 39

The number of teachers is still 252525 after the new appointment.

So, new total age is: 25×39=97525 \times 39 = 97525×39=975

  1. Age of newly appointed teacher

Let the age of the new teacher be xxx.

Then: 940+x=975940 + x = 975940+x=975 x=975−940=35x = 975 - 940 = 35x=975−940=35

  1. Check options

The age of the newly appointed teacher is 353535 years.

So the correct option is C.

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