A and B started a business by investing Rs. 2400 and Rs. 3600 respectively. At the end 4th months from the stat of the business, C joined with Rs. X. After 8 months from the start of the business, B withdrew Rs. 600. If C's share is Rs. 8000 in the annual profit of Rs. 22500, what was the amount C invested in the business ?

Solution(By Examveda Team)

A invests Rs. 2400 for 12 months
B invests Rs. 3600 for 8 months
And Rs. 3000 for 4 months
C invests Rs. X for 8 months
Ratio of profit of A, B and C
$$ \Rightarrow {\text{Profit of A}}$$   : $${\text{Profit of B}}$$   : $${\text{Profit of C}}$$
$$ \Rightarrow {\text{2400}} \times {\text{12}}$$   : $$\left( {3600 \times 8} \right)$$   + $$\left( {3000 \times 4} \right)$$   : $${\text{X}} \times 8$$
$$\eqalign{ & \Rightarrow 28800:40800:8{\text{X}} \cr & \Rightarrow 3600:5100:{\text{X}} \cr} $$
Given profit of C = Rs. 8000
And total profit of A, B and C = Rs. 22500
$$\eqalign{ & \therefore \frac{{{\text{X}} \times 22500}}{{3600 + 5100 + {\text{X}}}} = 8000 \cr & \Rightarrow \frac{{{\text{X}} \times 22500}}{{8700 + {\text{X}}}} = 8000 \cr} $$
$$ \Rightarrow 22500{\text{X}}$$   = $$69600000$$   + $$8000{\text{X}}$$
$$\eqalign{ & \Rightarrow 14500{\text{X}} = 69600000 \cr & \Rightarrow {\text{X}} = {\text{Rs}}.\,4800 \cr} $$