X and Y are partners sharing profits in the ratio of 3:2. They admit Z as a new partner for 1/5th share in the profits, which he acquires entirely fr…

X's old share = $3/5$. Z's share = $1/5$ (acquired entirely from X). X's new share = $3/5 - 1/5 = 2/5$. Y's new share = $2/5$. Z's share = $1/5$. To make denominators uniform ($5$), the new ratio is $2/5 : 2/5 : 1/5$, which is $2:2:1$ or multiplying by $5$, it is $10:10:5$ simplified to $2:2:1$ isn't matching options. Wait, let's recalculate: X's new share = $3/5 - 1/5 = 2/5$. Y's share = $2/5 = 8/20$. Z's share = $1/5 = 4/20$. X's new share = $2/5 = 8/20$. So ratio is $8:8:4$ which is $2:2:1$. Let's check option B: $12:8:5 ightarrow$ X's new share $3/5 - 1/5 = 2/5 = 12/30$, Y = $2/5 = 12/30$, Z = $1/5 = 6/30$. Let's use correct values: X's new share = $3/5 - 1/5 = 2/5$, Y's share = $2/5$, Z's share = $1/5$. Common denominator 5 gives $2:2:1$. None of A,B,C,D matches $2:2:1$ directly except if scaled. Let's re-evaluate option B: If X's old share is $3/5$ and he gives $1/5$, his new share is $2/5$. Y's share remains $2/5$. Z gets $1/5$. Ratio is $2/5 : 2/5 : 1/5 = 2:2:1$. Let's modify numbers: X and Y share $3:2$. Z is admitted for $1/5$th share acquired from X and Y equally. Let's fix the question: X and Y share $3:2$. Z is admitted for $1/5$ share. New ratio is $12:8:5$ if X sacrifices $1/10$ and Y sacrifices $1/10$. But here Z acquires entirely from X. X's new share = $3/5 - 1/5 = 2/5$. Y's share = $2/5$. Z's share = $1/5$. Thus ratio is $2:2:1$. Let's correct option C to $2:2:1$.