Raju started a business with Rs. 900. Kamal joined him after few months with an amount of 600. If the profits at the end of the year were divided in the ratio of 2:1, after how many months Kamal joined the business?

3 months

\(\frac{\text{Profit of Raju} }{\text{Profit of Kamal} }\)  = \(\frac{\text{Amount of Raju × months } }{\text{Amount of Kamal × months } }\)

\(\frac{2 }{1 }\) =  \(\frac{\text{900 × x} }{\text{600× y } }\) 

900x = 1200y

\(\frac{x}{y}\) = \(\frac{ 4}{ 3}\)

We know, Raju invested the amount for 12 months

so 4R → 12

1R = 3

in the same manner 3R → 9

Thus, as Kamal invested for 9 months we can say that he joined after 3 months.