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In a family, the sum of the ages of Father, Mother and Son is 90 years as on today. The age of father…

Let the son be \(s\); then the father is \(6s\) and the mother is \(90-7s\). The total doubles to 180 after \(t\) years where \(90+3t=180\), so \(t=30\), and then…

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In a family, the sum of the ages of Father, Mother and Son is 90 years as on today. The age of father is 6 times that of the son. The age of son will be half that of his father when the sum of the ages of all the members i.e father, mother and son becomes exactly twice the sum of their ages today. Find the present age of mother.

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Correct answer C

Let the son be ss; then the father is 6s6s and the mother is 90−7s90-7s. The total doubles to 180 after tt years where 90+3t=18090+3t=180, so t=30t=30, and then 2(s+30)=6s+302(s+30)=6s+30 gives s=7.5s=7.5. The father is 45 and the mother is 90−7(7.5)=37.590-7(7.5)=37.5 years.

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