In a partnership A invests \(\frac{1}{4}\)th of the total capital for \(\frac{1}{4}\) of the time, B invests \(\frac{1}{5}\)rd of the total capital for \(\frac{1}{2}\) of the time and C invests the rest of the capital for the whole time. Out of the profit of ₹2280, C's share is:

₹1760

For \(\frac{1}{4}\), \(\frac{1}{5}\) and \(\frac{1}{2}\):

Let the total capital = 20 Unit, and

Let the total time of investment = 4 months

ATQ,

                A        :       B         :    C

Inv.    :   20 × \(\frac{1}{4}\)    :   20 × \(\frac{1}{5}\)     :    Rest

Time  :   4 × \(\frac{1}{4}\)    :     4 × \(\frac{1}{2}\)    :    4

              A    :    B    :     C

Inv.    :   5    :    4    :    11

Time  :   1    :    2    :     4 

Profit:    5    :    8    :    44        [Profit ratio = Inv. ratio × Time ratio]

⇒ Total Profit = 57R = 2280

⇒ 1R = 40

⇒ C's Profit = 44R = 44 × 40 = 1760