Jack : How old are you, mamma?’ And how old is Dad ?
Mom : Let me think, Well, our three ages ( add up to exactly seventy years)
Dad : I am 6 times as old as you, my son.’
Jack : Shall I ever be half as old as you, papa?’
‘Yes, Jack; and when that happens our three ages will add up to exactly twice as much as to-day.
And, another interesting observation. One of us age today has got something to do with what happens in a leap year ?
Can you find their ages ?
Answers
Given : Information about ages of Jack , mom & dad
To find : age of all
Solution:
Let say Jack age = J
Father age = 6J
Mother age = 70 - (J - 6J) = 70 - 7J
let say after Y years Jack be half as old as papa
=> ( J + Y) 2 = (6J + Y)
=> 2J + 2Y = 6J + Y
=> 4J = Y
=> Y = 4J
Sum of Ages after Y years = 70 + 3Y
= 70 + 12J
70 + 12J = 2(70)
=> 12J = 70
=> J = 70/12
=> J = 35/6
=> Jack age = 35/6 Year
Father age = 35 Years
Mother age = 70 - 7J = 70 - 7*35/6 = 175/6 Years
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