In a partnership business, A and B invested in the ratio of 5 : 6. At the end of 8 months, A withdrew his capital. If they shared the eventual profit in the ratio of 5 : 9, then what is the number of months for which B invested his capital?

In a partnership business, A and B invested in the ratio of 5 : 6.

Let's assume the initial investment of A and B is '5y' and '6y' respectively.

At the end of 8 months, A withdrew his capital. If they shared the eventual profit in the ratio of 5 : 9.

Let's assume the number of months for which B invested his capital is 'z'.

$$\frac{5y\times\ 8}{6y\times\ z}\ =\ \frac{5}{9}$$

$$\frac{1\times\ 4}{1\times\ z}\ =\ \frac{1}{3}$$