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# A and B are partners sharing profit and losses in the ratio 3:2. They decided to admit C as a partner for 1/4th share. Find the new ratio and the sacrificing ratio?

In a partnership business, the ratio of the profits is proportional to the ratio of the money invested by each partner and the duration for which the money is invested.

## Answer: The new ratio is 3: 3: 2 and the sacrificing ratio is 9:1.

Let's use the condition given in the question to find the required ratios.

**Explanation:**

Since C was made a partner for 1/4th of the share, it means that the remaining share, that is, 3/4th of the share was invested by A & B.

Now, let's calculate A's and B's sacrifice in favour of C, as:

A's sacrifice in favour of C = 3/4 × 1/2 = 3/8

B's sacrifice in favour of C = 3/4 × 1/2 = 3/8

New ratio = A: B: C = 3/8 : 3/8: 1/4 = 3/8 : 3/8: 2/8 = 3: 3: 2.

We can now calculate the sacrificing ratio by using the relation: Sacrificing ratio = Old ratio - New ratio

Sacrifing ratio for A = 3/5 - 3/8 = 24/40 - 15/40 = 9/40

Sacrifing ratio for B = 2/5 - 3/8 = 16/40 - 15/40 = 1/40

Sacrificing ratio for A and B together is = 9/40 : 1/40 = 9:1

### Therefore, the new ratio is 3: 3: 2, and the sacrificing ratio is 9:1.

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