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Factfile:
The combined age of Megha and Anamika is 44 years.
Megha was twice as old as Anamika when Megha was half as old an Anamika will be when Anamika is 3-times as old as Megha was when Megha was three times as old as Anamika.
How old is Megha?

The age of Megha to that of Anamika must be as 5 to 3. And as the sum of their ages was 44, Megha was 27½ and Anamika 16½. One is exactly 11 years older than the other. I will now insert in brackets in the original statement the various ages specified: “Megha is (27½) twice as old as Anamika was (13¾) when Megha was half as old (24¾) as Anamika will be (49½) when Anamika is three times as old (49½) as Megha was (16½) when Megha was (16½) three times as old as Anamika (5½).” Now, check this backwards. When Megha was three times as old as Anamika, Megha was 16½ and Anamika 5½ (11 years younger). Then we get 49½ for the age Anamika will be when she is three times as old as Megha was then. When Megha was half this she was 24¾. And at that time Anamika must have been 13¾ (11 years younger). Therefore Megha is now twice as old—27½, and Anamika 11 years younger—16½