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

A) 28years

B) 36years

C) 34years

D) 35years

Answer

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Hint: Here we proceed the solution by finding the difference of ages of 8 men before increasing the age and after increasing the age and now by using the given condition we will find the age of the new man.

Complete step-by-step answer:

Here let us consider the average age of 8 men = x years

Now the total age of 8 men = 8x years

It is mentioned that the average age of 8 men has increased after 2 years.

So now the new average age = $(x + 2)$ years.

Therefore the total age of 8 men = $8(x + 2)$ years.

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

$ \Rightarrow 8x - 16 - 8x$ Years.

$ \Rightarrow \therefore 16$ Years.

Hence the difference of ages =6 years.

We clearly know that the new manager got replaced 20 years ago by an unknown person.

Now age of new man =$20 + 16 = 36$ years

From this we can clearly say that the new man's age is 16 years older to the unknown man by whom the new man is replaced.

Option B is the correct answer.

Note: In this problem we will neglect to find the total age of 8 men and also to find average and total age after 2 years. We have to make note that the new man is replaced by 20 years so after finding the difference of ages we have to add 20 years to it to get the new man's age.

Complete step-by-step answer:

Here let us consider the average age of 8 men = x years

Now the total age of 8 men = 8x years

It is mentioned that the average age of 8 men has increased after 2 years.

So now the new average age = $(x + 2)$ years.

Therefore the total age of 8 men = $8(x + 2)$ years.

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

$ \Rightarrow 8x - 16 - 8x$ Years.

$ \Rightarrow \therefore 16$ Years.

Hence the difference of ages =6 years.

We clearly know that the new manager got replaced 20 years ago by an unknown person.

Now age of new man =$20 + 16 = 36$ years

From this we can clearly say that the new man's age is 16 years older to the unknown man by whom the new man is replaced.

Option B is the correct answer.

Note: In this problem we will neglect to find the total age of 8 men and also to find average and total age after 2 years. We have to make note that the new man is replaced by 20 years so after finding the difference of ages we have to add 20 years to it to get the new man's age.

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