A and B entered into a partnership with investments in the ratio 3 : 5. After a few months, A withdrew and collected back his money. At the end of the year, they received profit in the ratio 2 : 5. After how many months did A withdraw?

8

A and B investments ratio = 3 ∶ 5.

Profit share ratio = 2 : 5

Let A invest for x months

According to the question,

\(\frac{(3 × x)}{ 5 × 12}\)  = \(\frac{(2)}{ 5}\)

⇒ \(\frac{(3x)}{ 60}\) = \(\frac{(2)}{ 5}\)

⇒ 15x = 120

⇒ x = 8

So, A invested for 8 months