The ratio of the investments of A and B in a business is 7 : 5, and the ratio of their profits at the end of a year is 2 : 5. If A invested the money for 6 months, then for how much time (in months) has B invested his money?

$$\eqalign{ & {\text{Time}} = \frac{{{\text{Profit}}}}{{{\text{Capital}}}} \cr & {\text{A's time}} = \frac{2}{7}{\text{ units}} \cr & {\text{B's time}} = \frac{5}{5} = 1{\text{ unit}} \cr & \frac{2}{7}{\text{ units}} = 6{\text{ months}} \cr & 1{\text{ unit}} = 6 \times \frac{7}{2} = 21\,{\text{months}} \cr} $$