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Question
A and B are partners in a firm sharing profits and losses in the ratio of 1:1. C is admitted. A surrenders `1/4`th share and B surrenders `1/5`th of his share in favor of C. Calculate the new profit sharing ratio.
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Solution
Old ratio of A and B = 1 : 1 or `1/ 2:1/ 2`
A’s sacrifice =`1/4xx1/2=1/8`
B’s sacrifice =`1/5 xx 1/2 = 1/10`
Sacrificing ratio of A and B =`1/8 : 1 /10`= 5 : 4
C’s share = A’s share + B’s share
= `1/8+ 1/10 = (5 + 4)/40= 9/40`
A’s new share = Old ratio – Sacrifice ratio
= `1/2 – 1/8 =(4 – 1)/8=3/8`
B’s new share = Old ratio – Sacrifice ratio
=`1/2 –1/10 = (5 – 1)/10 = 4/10`
Therefore, New ratio of A, B and C
= `3/8:4/10:9/40`
= 15 : 16 : 9
(Making denominator equal)
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