P and O enterinto a partnership with capitals in the ratio of 3:4. At the end of 10 months P with draws. If they share profit in the ratios 5:6 for how many months O’s capital was used ?

Solution

Let Ps and Os initial investment be 3x and 4x respectively.

P's investment was for 10 months so it will be proportional to (3x)(10) = 30x

let Q's investment be for 'm' months, so its proportional investment will be (4x)(m).

So according to investment profits will be divided in the ratio 30x : 4mx = 30:4m  

A/q 

=>  30:4m =  5:6

=> 30/4 =

=>  m= 9    

Hence O invested for 9 months.