Question

The average of the ages of three people - Raghav, Robert and Razia is 20. Three years later the average of their ages will b

Answer 1

Answer:

New average should be 23 years.

Step-by-step explanation:

Given,

The present average of the ages of three people - Raghav, Robert and Razia is 20.

From the properties of average :

• Average = ( sum of quantities ) / ( number of quantities )

Here,

• Average : 20 years.

• Number of people ( or quantities ) : 3

= > Average = ( sum of ages ) / ( number of ages )

= > 20 years = ( sum of ages ) / 3

= > 60 years = sum of ages

After 3 years : their ages will be increased by 3 years.

Total increase : 3 years + 3 years + 3 years i.e. 9 years.

Therefore :

= > Average of their ages after 3 years : ( sum of ages at present + 9 years ) / 3

= > New required average : ( 60 years + 9 years ) / 3 { from above sum of ages is 60 years }

= > New average : ( 69 years ) / 3

= > New average : 23 years

Hence the new average should be 23 years.

Answer 2

Given:

The average age of three people - Raghav, Robert and Razia is 20 years.

To find:

The average of their ages after three years.

Solution:

As we know that the average of 'n' number of observations is equal to the sum of observations divided by n.

This means

$average = \frac{sum \: of \:n \: observations}{n}$

Now,

As given,

we have

The average age of Raghav, Robert and Razia = 20 years.

Let the present age of Raghav, Robert and Razia be x, y and z years respectively.

So,

$\frac{x + y + z}{3} = 20$

$x + y + z = 60$

After 3 years,

the age of Raghav = (x + 3) years

the age of Robert = (y + 3) years

the age of Razia = (z + 3) years

So,

The average of their ages after three years

$= \frac{(x + 3) + (y + 3 ) + (z + 3)}{3}$

$= \frac{x + y + z + 9}{3}$

$= \frac{60 + 9}{3}$

$= \frac{69}{3}$

$= 23 \: years$

Hence, after three years, the average age of Raghav, Robert and Razia is 23 years.