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Question
Mrs. Goel is 27 years older than her daughter Rekha. After 8 years she will be twice as old as Rekha. Find their present ages.
Solution
Let the present age of Rekha be x years.
As Mrs. Goel is 27 years older than Rekha, the present age of Mrs. Goel will be (x + 27) years.
After 8 years:
Rekha's age = (x + 8) years
Mrs. Goel's age = (x + 27 + 8)
= (x + 35) years
According to the question:
(x + 35) = 2(x + 8)
or, x + 35 = 2 × x + 2 × 8 [On expanding the brackets]
or, x + 35 = 2x + 16
or, 35 − 16 = 2x − x [Transposing 16 to the L.H.S. and x to the R.H.S.]
or, x = 19
∴ Present age of Rekha = 19 years
Present age of Mrs. Goel = x + 27
= 19 + 27
= 46 years
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