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Numerical Questions · Q7

Q.A and B were partners in a firm sharing profits in 3:2 ratio. They admitted C for 3/7 share which he took 2/7 from A and 1/7 from B. Calculate new profit sharing ratio?

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The new profit-sharing ratio among A, B, and C is 11 : 9 : 15. This is found by subtracting the share sacrificed by each old partner from their original share, then expressing all three shares with a common denominator.

When a new partner is admitted, the old partners sacrifice a portion of their profit share in favour of the newcomer. The key idea is that the new ratio is simply the old ratio minus the sacrifice. Here, A and B were sharing profits in 3:2. C is admitted for 3/7 of the total profit. He takes 2/7 from A and 1/7 from B. That means A gives up 2/7 of the total profit, and B gives up 1/7.

So, A’s new share = his old share minus what he gave to C. A’s old share was 3/5 of the total (since 3:2 means A gets 3 parts out of 5). But careful: the sacrifice is given as a fraction of the total profit, not of A’s own share. So we work in fractions of the whole firm’s profit.

A’s old share = 3/5. He sacrifices 2/7 of the total profit. So A’s new share = 3/5 – 2/7. Similarly, B’s old share = 2/5, and he sacrifices 1/7, so B’s new share = 2/5 – 1/7. C gets 3/7 directly.

Now compute each:

A: 3/5 – 2/7 = (21 – 10)/35 = 11/35

B: 2/5 – 1/7 = (14 – 5)/35 = 9/35

C: 3/7 = 15/35 (since 3/7 = 15/35) …

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