Skip to content
Numerical Questions · Q4

Q.A, B and C are partners sharing profits in 2:2:1 ratio admitted D for 1/8 share which he acquired entirely from A. Calculate new profit sharing ratio?

Dnh Dd CbseNCERTSubjective· 3mImportance★★★★★
58% · 56/97 Questions
🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

The new profit-sharing ratio among A, B, C, and D is 11:16:8:5. D acquires his entire 1/8 share from A, so only A’s share reduces; B and C’s shares remain unchanged.

When a new partner is admitted, the existing partners sacrifice a portion of their share in favour of the new partner. The key here is that D gets his 1/8 share entirely from A. That means only A’s share changes — B and C keep their original shares exactly as they were.

The old ratio is A : B : C = 2 : 2 : 1. Let’s convert this into fractions of the total profit (which is 1). The total of the old ratio is 2 + 2 + 1 = 5. So:

  • A’s old share = 2/5
  • B’s old share = 2/5
  • C’s old share = 1/5

Now, D is admitted for 1/8 share. This 1/8 is taken entirely from A. So A sacrifices 1/8 of the total profit. Therefore:

  • A’s new share = A’s old share – sacrifice = 2/5 – 1/8
  • B’s new share = unchanged = 2/5
  • C’s new share = unchanged = 1/5
  • D’s new share = 1/8

We need to express all these fractions with a common denominator to get the new ratio. The denominators are 5 and 8 — LCM is 40.

Compute each:

  • A: 2/5 = 16/40; subtract 1/8 = 5/40 → 16/40 – 5/40 = 11/40
  • B: 2/5 = 16/40
  • C: 1/5 = 8/40
  • D: 1/8 = 5/40 …

Unlock everything free for 14 days

  • Full step-by-step solutions
  • Concept-first explanations
  • Methods, shortcuts & mistakes
  • PYQ mapping + timed mock tests

Full access for 14 days. No credit card required.