2 years ago a mother was 4 times as old as her son. 6 years from now her age will become more than double her son's age by 10 years. What is the present ratio of their ages?

Suppose the present age of son = P years
Present age of mother = Q years
According to question,
4 (P – 2) = Q – 2
⇒ 4P – 8 = Q – 2
⇒ 4P – Q = 6 ...(i)
2 (P + 6) + 10 = Q + 6
⇒ 2P + 12 + 10 = Q + 6
⇒ 2P – Q = –16 ...(ii)
From equations (i) and (ii)
P = 11
∴ Q = 4 × 11 – 6 = 38
Required the present ratio of their ages = 38 : 11