A, B and C invested in such a way that, A invested \(\frac{3}{8}\) of the total and B invested \(\frac{1}{3}\) of the total. Find their profit ratio.

9 : 8 : 7

Let total capital = 24 ( LCM of 8 & 3 ) 

A                     B                     C

24 × \(\frac{3}{8}\) = 9      24 × \(\frac{1}{3}\) = 8     24 - (9+8) = 7 ( profit of C ) 

Ratio of the profit = 9 : 8 : 7  

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