Question

The average age of five workers in a store was 36 years. When a new worker joined them, the average age of all of them became 37 years. How old was the new worker? ​

Answer 1

The new worker was 42 years old.

Given,

In a store,

the average age of 5 workers was 36.

After a new worker joined,

the average age of all of them became 37 years.

To find,

How old is the new worker?

Solution,

It can be seen here, that the average age of 5 workers is given to be 36 years.

We know that their average will be the sum of their ages divided by 5.

That is,

$\frac{sum \hspace{3} of \hspace{3} the \hspace{3} ages \hspace{3} of \hspace{3} 5 \hspace{3} workers}{5} =36$

So, we can say that

the sum of ages of 5 workers = 36 × 5 = 180.     ...(1)

Now, we can see that after a new worker joins, the number of workers will be 6. And, the new average is given to be 37 years.

Let the age of the new worker be 'x' years.

Then,

$\frac{(sum \hspace{3} of \hspace{3} the \hspace{3} ages \hspace{3} of \hspace{3} 5 \hspace{3} workers)+(x)}{6} =37$

⇒ (the sum of ages of 5 workers) + (x) = 37 × 6 = 222

Substituting the value of 'the sum of ages of 5 workers' from eq. (1) in the above equation, we get,

180 + x = 222

⇒ x = 222 - 180

⇒ x = 42.

Therefore, the new worker was 42 years old.

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Answer 2

Answer:

The age of new worker is $42$ years.

Step-by-step explanation:

It is given that the average age of five workers in a store was $36$ years.

A new worker joined them, the average age of all of them became $37$ years.

We need to determine the age of new worker.

Average is defined as the ratio of sum of observations to the number of observations.

For five workers,

$36=Sum/5$

$Sum=180$

When a new worker is added,

$37=New Sum/6$

$New Sum =222$

The new age is difference of two sums.

Age of new worker is $222-180$

$=42$ years.

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