Question 113

There is group of 8 teachers. One teacher leaves the group and a new teacher joins the group. Due to this, the average age of teachers becomes same as the average 2 years ago. If the member who left was aged 42, what is the age (in years) of new teacher ?


Let sum of the ages of 7 teachers (who remain constant) = $$7x$$ years

Average age of the original group = $$\frac{7x+42}{8}$$

Thus, average age 2 years ago = $$\frac{7x+42}{8}-2$$ ------------(i)

Let age of new teacher = $$y$$ years

Average age of new group = $$\frac{7x+y}{8}$$ -------------(ii)

According to ques, 

=> $$\frac{7x+42}{8}-2=\frac{7x+y}{8}$$

=> $$\frac{7x+42-16}{8}=\frac{7x+y}{8}$$

=> $$y=42-16=26$$

$$\therefore$$ Age of new teacher is 26 years

=> Ans - (D)

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