Q.A and B are partners sharing profits in the ratio 3:2. They admit C for 1/5th share in future profits, which he acquires equally from A and B. Calculate the new profit-sharing ratio and the sacrificing ratio.

Chinni's share = 1/6, so the remaining 5/6 is split 3:2 between Bunny and Sunny: Bunny 3/5 × 5/6 = 1/2, Sunny 2/5 × 5/6 = 1/3, Chinni 1/6. Taking a common denominator of 6 gives 3 : 2 : 1.

This is a standard AP Inter 2nd-year (Commerce) admission question, aligned with the NCERT/CBSE commerce curriculum.

Step 1 — Remaining share for old partners = 1 − 1/6 = 5/6.

Step 2 — Old partners keep their old ratio 3 : 2 of this remaining share.

• Bunny = 3/5 × 5/6 = 15/30 = 1/2
• Sunny = 2/5 × 5/6 = 10/30 = 1/3
• Chinni = 1/6

Step 3 — Express with common denominator 6:

• Bunny = 1/2 = 3/6
• Sunny = 1/3 = 2/6
• Chinni = 1/6

So the new ratio = 3 : 2 : 1 (total 6/6).

Krishna is admitted for 1/5 share, so the old partners together retain 1 − 1/5 = 4/5. As Ram and Shyam continue to share equally, each takes half of 4/5 = 2/5. Expressing all shares over a common denominator of 5 gives the new ratio 2 : 2 : 1.

Working

• Krishna's share = 1/5.
• Remaining share for Ram and Shyam = 1 − 1/5 = 4/5.
• Ram and Shyam share this equally (old ratio 1:1): each gets 4/5 x 1/2 = 2/5.

So Ram = 2/5, Shyam = 2/5, Krishna = 1/5. Taking the common denominator 5, the shares are 2/5, 2/5 and 1/5.

New profit-sharing ratio = Ram : Shyam : Krishna = 2 : 2 : 1.

Z takes 1/4; the remaining 3/4 is divided between X and Y in their old 1:2 ratio, giving a new ratio of 3 : 6 : 3 = 1 : 2 : 1.

Working

• Z's share = 1/4
• Remaining share for X and Y = 1 - 1/4 = 3/4
• This 3/4 is shared in the old ratio 1:2:
  • X = 3/4 x 1/3 = 3/12
  • Y = 3/4 x 2/3 = 6/12
• Z = 1/4 = 3/12
• New ratio = X : Y : Z = 3/12 : 6/12 : 3/12 = 3 : 6 : 3

Dividing throughout by 3: 1 : 2 : 1.