Thu February 28, 2013 By: Vrushali

The united ages of a man and wife are at present six times those of their children.Two yrs. ago, their united ages were ten times the united ages of their children.6 yrs. hence ,they will be three times the united ages of there children.How many children have they?

Expert Reply
Thu February 28, 2013
Let the united age of man and wife be x and that of children be y. Also, let them have n children. 
Now, as per question 
x = 6y
Also, 2 years ago,
the united age of man and wife would be (x - 4) (Need to subtract 2 from the ages of both man and wife and hence collectively 4 needs to be substracted from their combined ages)
Similarly, the united age of children would be (y - 2n)
Hence, x - 4= 10*(y-2n)
Substituting value of x 
6y - 4 = 10y - 20n
20n - 4 = 4y
y = 5n -1
Now, 6 years later, similarly, we will have
(x+12) = 3*(y+6n)
6y + 12 = 3y + 18n
3y +12 = 18n
3(5n-1) + 12 = 18n
9 = 3n
n = 3
So, they have 3 children. 
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