A, B, and C become partners in a business. A contributes \(\frac{1}{3}\)rd of the capitals for \(\frac{1}{4}\)th of the time. B contributes \(\frac{1}{5}\)th of the capital for \(\frac{1}{6}\)th of the time and C contribute rest of the capital for the whole time. If the profit is 1820, then the share of A in the profit is?

260

Let the total capital = 15 units

Investments:

A's = 15 × \(\frac{1}{3}\) = 5

B's = 15 × \(\frac{1}{5}\) = 3

C's = 15 - (5 + 3) = 7

Let the total time = 12 units

Time:

A's = 12 × \(\frac{1}{4}\) = 3

B's = 12 × \(\frac{1}{6}\) = 2

C's = 12

                A        :        B        :        C

Inv.           5        :        3         :       7

Time         3        :         2         :      12

           ---------------------------------------------

Profit       15       :        6          :      84

                5        :        2          :      28

Now,

Profit = (5 + 2 + 28)R = 1820

1R = 52

A's share = 5R = 5 × 52 = 260 Rs.