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Numerical Questions · Q6

Q.A, B and C are partners sharing profits in 3:2:2 ratio. They admitted D as a new partner for 1/5 share which he acquired from A, B and C in 2:2:1 ratio respectively. Calculate new profit sharing ratio?

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The new profit-sharing ratio among A, B, C, and D is 61 : 36 : 43 : 35.

When a new partner is admitted, the first thing we need to settle is the new profit-sharing ratio. The old partners sacrifice a portion of their share in favour of the incoming partner. The key here is to understand from whom the new partner gets his share and in what proportion the sacrifice is made.

D is admitted for a 1/5 share. This 1/5 is not taken equally from the old partners. Instead, D acquires this share from A, B, and C in the ratio of 2:2:1. This means:

  • A sacrifices 2/5 of D's share
  • B sacrifices 2/5 of D's share
  • C sacrifices 1/5 of D's share

The old ratio of A, B, and C is 3:2:2. Their old shares are:

  • A = 3/7
  • B = 2/7
  • C = 2/7

Now, we calculate the sacrifice made by each old partner. Sacrifice is the portion of their own share that they give up to D.

Watch out

A common mistake is to directly subtract the sacrifice from the old ratio without converting everything to a common denominator. Always work with fractions and find a common denominator before subtracting.

Step 1: Calculate the sacrifice of each old partner.

D's share = 1/5

Sacrifice ratio (A : B : C) = 2 : 2 : 1

  • A's sacrifice = (2/5) of (1/5) = 2/25
  • B's sacrifice = (2/5) of (1/5) = 2/25
  • C's sacrifice = (1/5) of (1/5) = 1/25

Step 2: Calculate the new share of each old partner.

New share = Old share – Sacrifice

  • A's new share = (3/7) – (2/25)
  • B's new share = (2/7) – (2/25)
  • C's new share = (2/7) – (1/25)

Step 3: Find a common denominator for all fractions.

The denominators involved are 7, 25, and 5 (for D's share). The LCM of 7, 25, and 5 is 175.

Convert all shares to denominator 175:

  • A's old share = 3/7 = 75/175
  • B's old share = 2/7 = 50/175
  • C's old share = 2/7 = 50/175 …

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