A and B enter into partnership with capitals in the ratio 5 : 6. At the end of 8 months A withdraws his capital. They received profits in the ratio 5 : 9. B invested the capital for

$$ Profit ratio [P] = Investment ratio [I] \times Time period [T]$$

A and B enter into partnership with capitals in the ratio 5 : 6

Investment ratio of A = 5

Investment ratio of B = 6

A withdraws his capital after 8 months 

Therefore, time period of A = 8 months

Assume time period of B as 'n'

Ratio of profit = $$ ratio of investment \times ratio of time period $$

Profit recieved by A and B in the ratio 5:9

$$ \frac{Profit ratio of A }{Profit ratio of B} = \frac{ Ia \times Ta}{Ib \times Tb} $$

Substituting,

$$ \frac{ 5 \times 8}{6 \times n} = \frac{5}{9} $$

Solving, n= 12 months