The sum of the present ages of a daughter and her mother is 52. If they both
live on till the daughter becomes as old as the mother is now, then the sum of
their ages will be 92. Find their present ages.
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Let x and y be the present age of mother and her daughter.
Therefore,
x+y=50
⇒x=50−y.....(1)
After 20 years, mother's age will be twice her daughter's age at the time.
x+20=2(y+20)
⇒x−2y=20.....(2)
From equation (1)&(2), we have
50−y−2y=20
3y=30
⇒y=10
Substituting the value of y in equation (1), we get
x=50−10=40
Hence the present age of mother and her daughter is 40 and 10 years respectively.
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