The ratio of investment of A and B is 15 : 22 and the ratio of their profit at the end of the year is 3 : 11 . If A invested the money for 2 months, then for how much time (in months) B invested his money?

5 months

                            A     :      B

Inv. Ratio    ⇒      15     :     22

Profit Ratio  ⇒        3     :     11       

Time Ratio  ⇒        \(\frac{3}{15}\)     :      \(\frac{11}{22}\)

                 ⇒        \(\frac{1}{5}\)      :      \(\frac{1}{2}\)

                 ⇒        2     :      5

Here,

According to the ratio, A invests his capital for 2 months (given), then B invest his capital for 5 months.

[*Time Ratio  = \(\frac{Profit\;ratio}{Inv.\;ratio}\)]