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Numerical Questions · Q12

Q.Rao and Swami are partners in a firm sharing profits and losses in 3:2 ratio. They admit Ravi as a new partner for 1/8 share in the profits. The new profit sharing ratio between Rao and Swami is 4:3. Calculate new profit sharing ratio and sacrificing ratio?

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The new profit-sharing ratio among Rao, Swami, and Ravi is 4:3:1, and the sacrificing ratio between Rao and Swami is 4:1.

When a new partner is admitted, the old partners give up a portion of their share in favour of the newcomer. The key here is to first determine the new profit-sharing ratio between the old partners (Rao and Swami) as given, then find Ravi’s share, and finally calculate how much each old partner sacrificed.

The new profit-sharing ratio between Rao and Swami is directly given as 4:3. Ravi is admitted for 1/8 share. So the combined share of Rao and Swami in the new firm becomes the remainder:

1 - 1/8 = 7/8.

Now, this 7/8 is split between Rao and Swami in the ratio 4:3. That means:

  • Rao’s new share = (4/7) × (7/8) = 4/8 = 1/2
  • Swami’s new share = (3/7) × (7/8) = 3/8
  • Ravi’s share = 1/8

Thus the new profit-sharing ratio is:

Rao : Swami : Ravi = 1/2 : 3/8 : 1/8 = 4/8 : 3/8 : 1/8 = 4:3:1.

Now, the sacrificing ratio is the difference between the old share and the new share for each old partner. The old ratio was 3:2 (Rao : Swami). Convert everything to a common denominator of 40 (which accommodates both the old fifths and the new eighths) for easy comparison:

Rao’s old share = 3/5 = 24/40

Rao’s new share = 1/2 = 20/40

Sacrifice by Rao = 24/40 - 20/40 = 4/40 = 1/10

Swami’s old share = 2/5 = 16/40

Swami’s new share = 3/8 = 15/40

Sacrifice by Swami = 16/40 - 15/40 = 1/40 …

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