Rohan , Sohan and Priya invested in such a way that, Rohan invested \(\frac{2}{5}\) of the total and Sohan invested \(\frac{3}{6}\) of the total. Find their profit ratio.

4 : 5 : 1

Let total capital = 30 ( LCM of 5 & 6 ) 

Rohan                     Sohan                     Priya

30 × \(\frac{2}{5}\) = 12      30 × \(\frac{3}{6}\) = 15     30 - (12+15) = 3 ( profit of Priya ) 

Ratio of the profit = 12:15: 3  = 4 : 5 : 1

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