Admission of M as a New Partner

The admission of M as a new partner will require a revaluation of the assets and liabilities of the partnership. This is done to ensure that the new partner's capital contribution is properly reflected in the partnership's books. Let's analyze the given information step by step.

Revaluation of Machinery

The machinery was overvalued by 10%. This means that the value of the machinery in the books of the partnership is 110% of its actual value. The original value of the machinery can be calculated using the formula:

Actual Value = Book Value / (1 + Overvaluation Percentage)
Actual Value = 66,000 / (1 + 10/100)
Actual Value = 66,000 / 1.10
Actual Value = 60,000

So, the actual value of the machinery is Rs. 60,000.

Revaluation of Creditors

The creditors were found only Rs. 81,000, which is less than the amount shown in the books (Rs. 84,000). This indicates that there is an overstatement of creditors in the books. The adjustment for this can be calculated as:

Adjustment = Book Value - Actual Value
Adjustment = 84,000 - 81,000
Adjustment = 3,000

So, the creditors need to be reduced by Rs. 3,000.

Revaluation of Stock

The stock was also overvalued, but the amount of overvaluation is not mentioned. However, it is mentioned that there is a loss on revaluation debited to Z's Capital Account of Rs. 1,500. This indicates that the stock is overvalued by Rs. 1,500. The adjustment for this can be calculated as:

Adjustment = Loss on Revaluation
Adjustment = 1,500

So, the stock needs to be reduced by Rs. 1,500.

Calculation of New Profit Sharing Ratio

Before admitting M as a partner, the profit sharing ratio between Y and Z is 3:2. Now, M is being admitted as a new partner, so the new profit sharing ratio will be 3:2:1 (Y:Z:M).

Calculation of M's Capital

To calculate M's capital, we need to consider the following:

1. Creditors: The reduced value of creditors is Rs. 81,000.
2. Machinery: The actual value of machinery is Rs. 60,000.
3. Stock: The reduced value of stock is Rs. 30,000 - Rs. 1,500 = Rs. 28,500.

M's Capital = Creditors + Machinery + Stock
M's Capital = 81,000 + 60,000 + 28,500
M's Capital = Rs. 169,500

Conclusion

In conclusion, the admission of M as a new partner requires the revaluation of assets and liabilities. The machinery was found to be overvalued by 10%, and the creditors were found to be less than the amount shown in the books. The stock was also overvalued, resulting in a loss on revaluation. Based on these adjustments, the new profit sharing ratio between Y, Z, and M is 3:2:1.