The present age of Amit = 17 years
5 years before , age of Rakesh = The present age of Amit - 5 years = 17 ? 5 = 12 years
? Age of Anil = age of Rakesh + 3 years = 12 + 3 = 15 years
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 .
Sum of ages of mother, daughter and son (i.e., 3 persons) = 87 years.
After 8 years , Sum of their ages = Sum of ages of mother, daughter and son + ( 8 x 3 ) = 87 + (8 × 3) = 87 + 24 = 111 years
Suppose the present age of B = P years
The present age of A - The present age of B = 2 years.
Therefore, the present age of A = P + 2 years
According to question,
Two years ago , 2( the present age of B - 2 years ) = the present age of A - 2 years
2 (P ? 2) = P + 2 ? 2
? 2P ? 4 = P
? 2P ? P = 4
? P = 4
Age of B = 4 years
Age of A = P + 2 = 4 + 2 = 6 years
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