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Mother was three times the age of her daughter 5 years ago. After 5 years, mother will be twice as old as her daughter. How old is the daughter today?
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- 5 years
- 10 years
- 15 years
- 20 years
Correct Option: C
Suppose the present age of daughter = P years
and, the present age of mother = Q years
According to questions,
5 years ago , 3 × ( the present age of daughter - 5 ) = ( the present age of mother - 5 )
3 (P – 5) = (Q – 5)
⇒ 3P – 15 = Q – 5
⇒ 3P – Q = 10 .......(i)
After five years , 2 × ( the present age of daughter + 5 ) = ( the present age of mother + 5 )
2 (P + 5) = Q + 5
⇒ 2P + 10 = Q + 5
⇒ 2P – Q = –5 .......(ii)
From equations (i) and (ii) , we get
3P – 2P = 10 – (–5)
⇒ P = 15 years
Hence, the present age of daughter is 15 years .
