The average age of $8$ men is increased by $2$ yr when one of them whose age is $20$ yr is replaced by a new man. What is the age of the new man

28

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Solution

The correct option is C $36$ yr
Let the average age of $8$ men $= x$ yr

Total age of $8$ men $= 8 x$ yr

Now, new average age $= (x + 2)$ yr

Total age $= 8 (x + 2)$ yr

Difference of ages $= 8 (x + 2) - 8 x$

$= 8 x + 16 - 8 x = 16$ yr

Age of new man $= 20 + 16 = 36$ yr

So, the new man is $16$ yr older to the man by whom the new man is replaced.

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The average age of 8 men is increased by 2 yr when one of them whose age is 20 yr is replaced by a new man. What is the age of the new man

The correct option is C 36 yrLet the average age of 8 men =x yrTotal age of 8 men =8x yrNow, new average age =(x+2) yrTotal age =8(x+2) yrDifference of ages =8(x+2)−8x=8x+16−8x=16 yrAge of new man =20+16=36 yrSo, the new man is 16 yr older to the man by whom the new man is replaced.

The average age of $8$ men is increased by $2$ yr when one of them whose age is $20$ yr is replaced by a new man. What is the age of the new man