The average age of 14 girls and their teacher is 15 years If the teacher 39 s age is excluded the av...........

Quantitative Aptitude (HARCO) Average

The average age of 14 girls and their teacher is 15 years. If the teacher's age is excluded, the average reduces by 1. What is the teacher's age?

35 years

32 years

30 years

29 years

Sum of ages of all girls = X

Age of the teacher = Y

We know that average age of all girls = X ÷ 14.

And, average age of the girl's ages and teacher's age = 15

We know that average age of all girls is 1 year less that average age when the teacher is also included.

So we can then write this as :

(X + Y ) ÷ 15 = 15 (Since we are taking average age of 15 people, we divide by 15).

or X + Y = 15 * 15 = 225

or X = 225 - Y

Average age of all girls = X * 14 (Sum of ages of the girls divided by number of girls).

We also know that this value is 1 less that the average age of girls + teacher.

Therefore, X ÷ 14 = 14, or (225 - Y) = 196

Which means, Y = 225 - 196 = 29

Hence, option 4 is the correct answer.

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