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A father’s age is equal to the sum of the ages of his 3 children. In 9 years his age will be equal to the sum of the two eldest son’s ages and 3 years after that his age will be equal to the sum of the ages of his eldest and youngest children. Again 3 years after that his age will be equal to the sum of the ages of his two youngest children. Find the father’s present age ?

A father’s age is equal to the sum of the ages of his 3 children. In 9 years his age will be equal to the sum
of the two eldest son’s ages and 3 years after that his age will be equal to the sum of the ages of his eldest
and youngest children. Again 3 years after that his age will be equal to the sum of the ages of his two
youngest children. Find the father’s present age ?

Grade:10

1 Answers

Ritika Das
105 Points
7 years ago
Let the father’s age be a years and that of his oldest, younger and youngest children be x years ,y years, and z years respectively.
According to the problem,as everyone age grew by time,
a=x+y+z in the present year;.......(1)
a+9=(x+9)+(y+9) after 9 years;
or,a=x+y+9........................(2)
a+9+3=(x+9+3)+(z+9+3) after (9+3) years;
or, a=x+z+12...............................(3)
and a+9+3+3=y+z after (9+3+3) years;
or, a=y+z+15...............................(4)
Putting value of (2) in (1) we get z=9 years.
Putting value of (3) in (1) we get y=12 years.
Putting value of (4) in (1) we get x=15 years.
Putting all the ages of the children in (1) we get a=36 years.

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