Sum

R and S are partners sharing profits in the ratio of 5 : 3. T joins the firm as a new partner. R gives 1/4th of his share and S gives 1/5th of his share to the new partner. Find out new profit-sharing ratio.

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#### Solution

Old Ratio = R : S

= 5 : 3

Sacrificing Ratio = Old Ratio × Surrender Ratio

R's = `5/8 xx 1/4 = 5/32`

S's = `3/8 xx 1/5 = 3/40`

New Ratio = Old Ratio − Sacrificing Ratio

R's = `5/8 - 5/32 = 15/32`

S's = `3/8 - 3/40 = 12/40`

T's share = R's sacrifice + S's Sacrifice

= `5/32 + 3/40 = [ 25 + 12 ]/160 = 37/160`

New Profit Sharing Ratio = R : S : T

= `15/32 : 12/40 : 37/160`

= `[ 75 : 48 : 37]/160`

∴New Profit Sharing Ratio = 75 : 48 : 37

Concept: Retirement and Death of a Partner - Calculation of New Profit Sharing Ratio

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