(Old Partners sacrifion in a Particular Proportion).
X and Y are partners sharing profits and losses in the ratio of 7 : 5. They admit Z, a new partner, who acquires 1/12th from X and 1/6th from Y as his share.
Calculate new profit-sharing ratio and the sacrificing ratio.

Explanation

Calculation of New profit-sharing Ratio:
Old profit-sharing ratio of X and Y 7 : 5
Z acquires his share 1/12th from X and 1/6th from Y.
His total share comes to `(1)/(12)+(1)/(6)=(1+2)/(12)=(3)/(12)`
X's share after giving `(1)/(12)th "share to" Z=(7)/(12)-(1)/(12)=(6)/(12)`
Y's share after giving `(1)/(6)th` share to `Z=(5)/(12)-(1)/(6)=(5-2)/(12)=(3)/(12)`
Hence, New Profit-sharing Ratio of X, Y and Z =6/12: 3/12: 3/12=2:1:1.
sacrificing Ratio:
`"X Sacrificed"=(1)/(12),"Y Sacrificed"=(1)/(6)`
Hence, Sacrificing Ratio of X and Y `=(1)/(12):(2)/(12)or1:2`.