The ratio of investment of A and B is 16 : 21 and the ratio of their profit at the end of the year is 2 : 3 . If A invested the money for 7 months, then for how much time (in months) B invested his money ?

8 months 

                            A     :      B

Inv. Ratio    ⇒       16    :     21

Profit Ratio  ⇒        2     :      3       

Time Ratio  ⇒        \(\frac{2}{16}\)     :      \(\frac{3}{21}\)

                 ⇒        \(\frac{1}{8}\)      :      \(\frac{1}{7}\)

                 ⇒        7     :      8

Here,

According to the ratio, A invests his capital for 7 months (given), then B invest his capital for 8 months.

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