A , B and C invested in such a way that, A invested \(\frac{3}{7}\) of the total and B invested \(\frac{1}{6}\) of the total. Find their profit ratio.

18 : 7 : 17

Let total capital= 42 ( LCM of 7 & 6 ) 

A                     B                     C

42 × \(\frac{3}{7}\) = 18      42 × \(\frac{1}{6}\) = 7     42 - (18+7) = 17 ( profit of C ) 

Ratio of the profit = 18 : 7 : 17  

[*Profit ratio is same when time is constant for each partner]