A, B and C enter into a partnership with capitals in the ratio $$\frac{2}{3} : \frac{3}{5} : \frac{5}{6}$$. After 8 months, A increases his share of capital by 25%.If at the end of the year, the total profit earned is ₹5,820, then the share of C in the profit is:

Initial Capital of A:B:C = $$\frac{2}{3} : \frac{3}{5} : \frac{5}{6}$$

A'1 share for 8 months = $$\dfrac{2}{3}$$part

and for next 4 month = $$ \dfrac{2}{3}+ \dfrac{2}{3}\times 25%$$

$$\Rightarrow \dfrac {4}{6} + \dfrac{1}{6} = \dfrac{5}{6} $$

So A's one months Value = \dfrac{2}{3}\times 8 + \dfrac{5}{6}\times 4 $$

$$\Rightarrow \dfrac{16+10}{3}= \dfrac{26}{3} $$

B's  one months value = $$\dfrac{3}{5}\times 12 = \dfrac{36}{5}$$

$$\Rightarrow \dfrac{5}{6 }\times 12 = 10 $$

then profit sharing ratio = $$\dfrac{26}{3}: \dfrac{36}{5}:\dfrac{10}{1} $$

$$\Rightarrow 130: 108:150 $$

total profit = Rs 5820 

then share C's  = $$\dfrac{5820}{130+108+150} \times 150 $$

$$\Rightarrow \dfrac{5820}{388}\times 150 $$

$$\Rightarrow 2250 $$

$$\Rightarrow Rs 2250 $$Ans