Partnership

Q) A and B enter into a partnership with Rs 50000 and Rs 60000 .C joins them after x months contributing Rs 70000 and B leaves x months before the end of the year .If they share ratio of 20:18:21 then find the valuer of x?

We calculating the ratio for 12 months
A's contribution= 50000*12
since B left x months before the end of the year so his contribution=60000(12-x)
and same for C= 70000(12-x)
their ratios
      50000*12:60000(12-x):70000(12-x)
    =>    60  : 6(12-x)   : 7(12-x)
Now given ratio is 20:18:21
so we divide by 3 in the ratio
    =>    20  : 3(12-x)   : 7(12-x)/3
on comparing the B's ratio with the given one we get
         3(12-x)=18
             x=3