A and B invested a sum of money in the ratio of 3 : 5. After a few months, A withdrew and collected back his money. At the end of the year, they received profit in the ratio of 2 : 5. After how many months A withdrew his money?

8

                          A       :        B

Inv. ratio  →       3       :        5

Time         →       t        :        12      

Profit        →      2        :       5               (given)

Here,

(Profit = Inv. × time)

⇒ \(\frac{2}{5}\) = \(\frac{3\;×\;t}{5\;×\;12}\)

⇒ 3 t = 24

⇒ t = 8

Hence, A invest his capital for 8 months,

So, A withdrew after = 8 Months