Twice Manvi's age plus Tanvi's age is 37 years. Tanvi's father is twice as old as Tanvi, and Manvi's brother is 5 years older than Manvi. The sum of the ages of Tanvi's father and Manvi's brother is 43 years. Find the sum of the ages (in years) of Manvi and Tanvi.
25
Let Manvi be M years and Tanvi be T years old. Then 2M + T = 37.
Tanvi's father is 2T and Manvi's brother is M + 5, so 2T + M + 5 = 43, i.e. M + 2T = 38.
Adding the two equations: 3M + 3T = 75, so M + T = 25.
Check: solving gives M = 12 and T = 13; 2 × 12 + 13 = 37, and the father (26) plus the brother (17) is 43, as given.
Hence, 25.
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