Aakash and Sumit are partners in a business. Aakash contributes \(\frac{2}{5}\) of the capital for 12 months and Sumit received \(\frac{3}{7}\) of the profit. For how long Sumit's money was used?

6 months

                Aakash            Sumit             Total

Capital        2                     3         ⇒       5

Time           12                   x

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

Profit           4                    3         ⇒       7

 Now, ATQ

\(\frac{2 × 12}{3 × x}\) = \(\frac{4}{3}\)

x = \(\frac{12 × 2 }{4}\)

x = 6 months