A started a business with the capital of Rs. 500. After 2 months B joined A with Rs. 400. 6 months after the business started C joined with Rs. 800. If the total profit earned at the end of the year is Rs. 444 find the share of their profit ?

A started a business with the capital of Rs. 500. After 2 months B joined A with Rs. 400. 6 months after the business started C joined with Rs. 800. If the total profit earned at the end of the year is Rs. 444 find the share of their profit ? Correct Answer Rs. 180, Rs. 120, Rs. 144

	A	:	B	:	C
Capital	500	:	400	:	800
	×	:	×	:	×
Time	12	:	10	:	6
Profit	6000	:	4000		4800
	15	:	10	:	12

$$\eqalign{ & {\text{According to the question,}} \cr & \left( {15 + 10 + 12} \right){\text{units}} = {\text{Rs}}{\text{.}}\,{\text{444}} \cr & {\text{37 units}} = {\text{Rs}}{\text{. 444}} \cr & 1{\text{ unit}} = \frac{{444}}{{37}}{\text{ = Rs}}{\text{. 12}} \cr & {\text{Profit of A}} = 12 \times 15 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,{\text{180}} \cr & {\text{Profit of B}} = 12 \times 10 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,{\text{120}} \cr & {\text{Profit of C}} = 12 \times 12 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,{\text{144}} \cr} $$