In a partnership A invests \(\frac{1}{6}\)th of the total capital for \(\frac{1}{6}\) of the time, B invests \(\frac{1}{3}\)rd of the total capital for \(\frac{1}{3}\) of the time and C invests the rest of the capital for the whole time. Out of the profit of ₹2300, find the difference b/w A and B's share.

₹300

For \(\frac{1}{6}\) and \(\frac{1}{3}\):

Let the total capital = 6 Unit, and

Let the total time of investment = 6 months

ATQ,

                A      :       B          :    C

Inv.    :   6 × \(\frac{1}{6}\)    :    6 × \(\frac{1}{3}\)     :    Rest

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

              A    :    B    :    C

Inv.    :   1    :    2    :    3

Time  :   1    :    2    :    6  

Profit:    1    :    4    :    18        [Profit ratio = Inv. ratio × Time ratio]

⇒ Total Profit = 23R = 2300

⇒ 1R = 100

⇒ Difference b/w A and B's Profit = 3R = 3 × 100 = 300