Mother’s age is 4 times her daughter’s age. 16 years hence mother’s age will be twice her daughter’s age at that time. Find their present ages. Ans. Mother’s present age ; 32 years. daughter’s present age : 8 years
Answer: Mother is 32 years old and daughter is 8 years old.
Let the daughter's present age be \(x\) years and the mother's \(y\) years.
\[y = 4x \quad\text{(1)}\]
After 16 years, the mother's age is twice the daughter's:
\[y + 16 = 2(x + 16) \quad\text{(2)}\]
Substitute (1) in (2):
\[4x + 16 = 2x + 32 \Rightarrow 2x = 16 \Rightarrow x = 8\]
Then \(y = 32\).
Check: after 16 years, 48 = 2 × 24.
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