Raja and Ram are partners sharing profits in ratio 3 : 1. Ashok is admitted for $${\frac{1}{4}^{{\text{th}}}}$$ share in profits. New profit sharing ratio between Raja, Ram and Ashok is?

The correct answer is A. 9 : 3 : 4.

Initially, Raja and Ram share profits in the ratio 3 : 1. This means that Raja gets 3 parts of the profit and Ram gets 1 part of the profit. When Ashok is admitted, he gets a $\frac{1}{4}$ share in the profits. This means that the new profit sharing ratio is 3 : 1 : $\frac{1}{4}$. To express this in a simpler form, we can multiply each ratio by 4 to get 12 : 4 : 1. This can also be written as 9 : 3 : 4.

Here is a step-by-step solution:

1. Let x be the total profit.
2. Raja’s initial share = 3x/4
3. Ram’s initial share = x/4
4. Ashok’s share = x/4
5. The new profit sharing ratio = 3x/4 : x/4 : x/4 = 9 : 3 : 4

Here is a brief explanation of each option:

• Option A: 9 : 3 : 4 is the correct answer. This is the new profit sharing ratio after Ashok is admitted.
• Option B: 3 : 1 : 1 is the initial profit sharing ratio between Raja and Ram. This is not the new profit sharing ratio after Ashok is admitted.
• Option C: 2 : 1 : 2 is not the new profit sharing ratio after Ashok is admitted.
• Option D: 3 : 4 : 9 is not the new profit sharing ratio after Ashok is admitted.