CAT2009-5

Question

The average age of a couple is $25$ years. The average age of the family just after the birth of the first child was $18$ years. The average age of the family just after the second child was born was $15$ years. The average age of the family after the third and the fourth children (who are twins) were born was $12$ years. If the present average age of the family of six persons is $16$ years, how old is the eldest child?

1. $6$ years
2. $7$ years
3. $8$ years
4. $9$ years

Answer 1

Ans : 9yrs

Let H: husband age; W: Wife age ; C_i = Age of i^th child

given (H + W)/2 = 25 => H+W = 50

Here we can take age of husband and wife as 25yrs each because finally we substitute (H+W),so it doesn't affect the result.

Let first child was born after x yrs.

Avg. age of family after first child = (H+x)+ (W+x) + C₁  /3 = 18 =>H+W+2x + C₁  = 54 => 50 + 2x + 0 = 54 => x = 2

Hence first child was born after 2yrs.

Calculating in same way ,you will get following:

2nd child was born after 2yrs,3rd & 4th child was born after 3yrs, and 4th twin .

Now let y yrs passed after twins were born and given present avg. age of family = 16

(32+y + 32+y + 5+y+3+y+0+0)/6 = 16 => y = 4

So we fill following table. 

Age--------------->

Husband	Wife	1st Child	2nd Child	3rd child	4th child
25	25	NOT BORN	NOT BORN	NOT BORN	NOT BORN
27	27	BORN	NOT BORN	NOT BORN	NOT BORN
29	29	2	BORN	NOT BORN	NOT BORN
32	32	5	3	BORN	BORN
36	36	9	7	4	4

Hence age of eldest child i.e child 1 =  9yrs.