A and B are partners in a business. A contributed $\frac{1}{3}$ of the capital for 9 months and B received $\frac{2}{5}$ of the profit. For how long was B's money used in the business?

3 months

Investment ratio × time = Profit ratio

                               A            B

Investment               1      :     2

                               9      :     x

-----------------------------------------------

                               3      :     2

\(\frac{  1 ×9  }{ 2 × x }\) = \(\frac{3}{2}\)

x = 3 months

So, B invested for 3 months

The correct answer is Option (3) → 3 months