P and Q are partners sharing profit in 2:1 ratio. They admitted R into partnership giving him 1/5th share which he acquired from P and Q in a 2:1 ratio. New Profit Sharing Ratio will be:

8:4:3

Old ratio = 2:1
R's share = 1/5
Sacrificing ratio =2:1
New share of P = 2/3 - (1/5 x2/3)
                         = 2/3 - 2/15
                         = 8 /15
New share of  Q =1/3 - (1/5 X1/3)
                           = 1/3 -1/15
                           = 4/15
NEW RATIO = 8/15 :4/15:1/5
                   =8:4:3