# Aptitude - Average - Discussion

Discussion Forum : Average - General Questions (Q.No. 2)
2.
A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
 28 4 years 7
 31 5 years 7
 32 1 years 7
None of these
Explanation:
Required average
 = 67 x 2 + 35 x 2 + 6 x 3 2 + 2 + 3
 = 134 + 70 + 18 7
 = 222 7
 = 31 5 years. 7

Video Explanation: https://youtu.be/OXLnoItd0MA

Discussion:
66 comments Page 1 of 7.

Praju said:   8 years ago
@Neha and @Pratiksha.

Average = sum of the given no /total no.

In the given question you have given the average of 2 grandparents, 2parents and 3 grandchildren. Now you have to calculate the average of all family members.

From the average, we can calculate sum of the numbers as;

Average = sum of the given number/total number.
Sum of the given numbers =avg * total number.

Total number = sum of the given number/avg.

From above data, we can calculate sum of numbers

Avg of 2 grandparents = 67.
Total no grandparents = 2.
Sum of the ages of grandparents = ?

According to formula,
Avg = sum of total no/total no.
Sum of total no = avg * total no.
Sum of total no = 67 * 2 = 134.

Sum of ages of two grandparents is 134 likewise,
Sum of 2 parents is = 35 * 2 = 70.
Sum of three grandchildren is = 6 * 3 = 18.

Now we have to calculate all average of the family.
Total no of family members are 7 i.e. 2 grandparent ,2parents, 3grandchildren
2 + 2 + 3 = .

Avg of total family members = sum of the ages of family members/total no of family members.

As we count sum of ages all family members,
(134 + 70 + 18)/7 = 222/7 = 31.6 = 31 5/7.
(3)

Dhivya R said:   9 years ago

Because the given question is 2 grandparents, 2 parents, 3 grandchildren.

Average age of grandparents is 67. So age of two grandparents is 67*2 = 134. Average age of parents is 35. So age of two parents is 35*2 = 70. Average age of three grandchildren is 6. So age of three grandchildren is 6*3 = 18.

Average = Sum of observation/Number of observation.

Average = 134+70+18/2+2+3.

Average = 222/7.

We convert ordinary fraction into mixed fraction.

So finally we get average = 31 5/7.

Grace said:   6 years ago
@Ravisinh Mori, @Banita and @Ankur Mishra.

We must emphasise on the term grandparent. When we are talking about only one person (either mother or father of a grandchild) it is termed as a grandparent.

While we are talking about two people (both mother and father of a grandchild) it is termed as grandparents. Hence 2 is mentioned just to clarify that the question is talking about 2 people.

Because they have used it as a plural with plural.
(1 person=grandparent & 2 person=grandparents).

Seenivasan.MG said:   3 years ago
Agree @Pavithra Uh.

Parent means (Mom or Dad) , parents means (both Mom and Dad) , grandparents means (grandma and grandpa (single set)).

Single set = (grandpa and grandma) , Double set = ( (Grandpa and Grandma) , (Grandpa and Grandma) ) likewise.

In question, the Average age of Grandparents (Single set) is 67.

So, we multiply by 2.

Suppose in our question 3 Grandparents means we multiplied by 3.

Correct me, If I am wrong.
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Surendra said:   10 years ago
We know that answer is 222/7.

Verify the options: all options consist the denominator 7.
We have the numerator 222.

In 222 units place is 2.
For 31 5/7 we have to multiply 31 and 7 and to the result we have to add 5.

In 31x7 the units place is 7(since 1x7=7).
To that 7 we will add 5, the result is 12 in which the units place is 2 which matches with the units place of 222.

For all other options the units place is not 2.

@Eric: The numbers are not equal, grandparents are 2, parents are also 2 but children are 3. so don't take avg figure.

Grand parents avg age of 2 = 67, but 2 people are there so 67*2.
Parents avg age of 2 = 35, 2 people are two so 35+35 or 35*2.
Children are 3 avg age = 6, people are three so 6+6+6 or 6*3.

If in the question if he said children also two then you can take avg directly.

Faizal Hussain said:   9 years ago
Please explain, why for parents also your multiplying by 2 and for two grandparents also multiplying by 2. Why can't we consider like this.

For parents means = Father and mother, hence its multiplied by 2.

For 2 grandparents means = Father's father, father's mother, mother'father, mothers mother, hence it should be 4.

Faizan said:   10 years ago
Now see, let denote grand parent by gp,

The average age of grandparents is given as 67,
Which means (gp1+gp2)/2 is equal to 67.

Similarly,
(p1+p2)/2 is equal to 35.

Similarly,
(gc1+gc2)/2 is equal to 6.

We are required to find,
(gp1+gp2+p1+p2+gc1+gc2)/7 is ?

So we found numerator by this way as:
67*2+35*2+6*2 = numerator.

Consider, Average age of grandparents is given i.e. avg = 67.

Also number of grandparents = 2.

By definition of average.

Average = total observations of all objects/total no of objects.

Let sum of individual ages of grandparents = X.

In this case,

Substituting in above formula,

67 = X/2.

Hence, X = 67x2.

And rest is average concept.

Thanks :).

Er. Ashish Yadav said:   9 years ago
Required average = 67 x 2 + 35 x 2 + 6 x 3.
-----------------------
2 + 2 + 3
= 134 + 70 + 18
---------------
7
= 222
-----
7
= 31 5 years.
-
7

Divide:

7)222(31
- 21
-------
12
- 7
-------
5
-------
so that is right it like 31 5
--------------------------
7
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