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?

12 months

The ratio of capital of A and B = 5 : 6

A's time = 8 months

A's profit : B's profit = 5 : 9    .........(i)

According to the question,

A's profit : B's profit = 5 × 8 : 6 × t = 40 : 6t = 20 : 3t   ........(ii)

*(Profit ratio = Investment ratio × time ratio)

Now, from eq. (i) and (ii),we get

⇒ 5 : 9 = 20 : 3t

⇒ t = (180)/(15)

⇒  t = 12