In a partnership A invests \(\frac{1}{3}\)th of the total capital for \(\frac{1}{2}\) of the time, B invests \(\frac{1}{5}\)rd of the total capital for \(\frac{1}{3}\) of the time and C invests the rest of the capital for the whole time. If the difference between profit of A and C is Rs.8100, then find the profit of B.

Rs. 1800

For \(\frac{1}{3}\), \(\frac{1}{5}\) and \(\frac{1}{2}\):

Let the total capital = 15 Unit, and

Let the total time of investment = 6 months

ATQ,

                A        :       B         :    C

Inv.    :   15 × \(\frac{1}{3}\)    :   15 × \(\frac{1}{5}\)     :    Rest

Time  :   6 × \(\frac{1}{2}\)    :     6 × \(\frac{1}{3}\)    :    6

              A    :    B    :     C

Inv.    :   5    :    3    :     7

Time  :   3    :    2    :     6 

Profit:  15    :    6    :    42        [Profit ratio = Inv. ratio × Time ratio]

⇒ Difference b/w A and C = 27R = 8100

⇒ 1R = 300

⇒ B's Profit = 6R = 6 × 300 = 1800