\(\frac{1}{5}\) of A's capital = \(\frac{1}{6}\) of B's capital = \(\frac{2}{3}\) of C's capital. If they invest for three years, then find the profit of A after three years out of the total profit of 7500 .

3000

\(\frac{1}{5}\)A  = \(\frac{1}{6}\)B = \(\frac{2}{3}\)C  

6A = 5B , 3B = 12C 

A   :    B               B    :    C

5   :     6              12   :    3

On solving →    A  :   B  :   C

                     10  :   12  :   3

Note → If the period of all the investors is the same then there is no effect of time on profit

                    A    :      B     :     C

                   10   :    12     :     3     = 25R

25R = 7500

A's profit → 10 → \(\frac{7500}{25}\) × 10 = 3000