[51 years] The average age of 36 students in a group is 14 years. When teachers age is included to it, the aver

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The average age of 36 students in a group is 14 years. When teachers age is included to it, the average increases by one. Find out the teachers age in years?

51 years

49 years

53 years

50 years

Explanation:

average age of 36 students in a group is 14

Sum of the ages of 36 students = $ 36 \times 14 $

When teachers age is included to it, the average increases by one

=> average = 15

Sum of the ages of 36 students and the teacher = $ 37 \times 15$

Hence teachers age

$= 37 \times 15 - 36 \times 14$

$= 37 \times 15 - 14(37 - 1)$

$= 37 \times 15 - 37 \times 14 + 14$

= 37(15 - 14) + 14

=37 + 14

= 51

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