$10$ years ago, Chandravati's mother was $4$ times older than her daughter. After $10$ years, the mother will be twice older than the daughter. The present age of Chandravati is

Let the present ages of Chandravati and her mother be C and M. The problem gives the equations M - 10 = 4(C - 10) and M + 10 = 2(C + 10). Simplifying these gives M = 4C - 30 and M = 2C + 10. Setting them equal gives 4C - 30 = 2C + 10, so 2C = 40 and C = 20.

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