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Numerical Questions · Q9

Q.Radha and Rukmani are partners in a firm sharing profits in 3:2 ratio. They admitted Gopi as a new partner. Radha surrendered 1/3 of her share in favour of Gopi and Rukmani surrendered 1/4 of her share in favour of Gopi. Calculate new profit sharing ratio?

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The new profit-sharing ratio among Radha, Rukmani, and Gopi is 4 : 3 : 3.

When a new partner is admitted, the old partners sacrifice a portion of their share in favour of the incoming partner. The key is to first find out what each old partner surrenders (gives up), then subtract that from their original share to get their new share. Gopi’s share is simply the sum of what he receives from Radha and Rukmani.

Why this treatment?

The sacrifice is always a fraction of the old partner’s own share, not of the total profit. So “Radha surrendered 1/3 of her share” means she gives up 1/3 of 3/5 (her original share), not 1/3 of the whole firm’s profit. This is a common point of confusion — many students mistakenly treat the surrendered fraction as a fraction of the total, which leads to a wrong ratio.

Let’s work it step by step.


Step 1: Write the old profit-sharing ratio

Radha : Rukmani = 3 : 2

So,

Radha’s old share = 3/5

Rukmani’s old share = 2/5


Step 2: Calculate the sacrifice made by each old partner

Radha surrenders 1/3 of her share:

Sacrifice by Radha = 1/3 × 3/5 = 3/15 = 1/5

Rukmani surrenders 1/4 of her share:

Sacrifice by Rukmani = 1/4 × 2/5 = 2/20 = 1/10


Step 3: Calculate the new share of each old partner

New share = Old share – Sacrifice

Radha’s new share:

= 3/5 – 1/5 = 2/5

Rukmani’s new share:

= 2/5 – 1/10

= 4/10 – 1/10 = 3/10


Step 4: Calculate Gopi’s share

Gopi receives the sacrifices from both old partners:

Gopi’s share = 1/5 + 1/10 = 2/10 + 1/10 = 3/10

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