On the date of admission of a partner, there was a balance of $\text{₹ }45,000$ in the account of machinery. It was found undervalued by $10\%$. The value of machinery will appear in the new Balance Sheet at:

Let the true book value of the machinery be $X$.The asset is currently undervalued by $10\%$, which means the existing book value is equal to $90\%$ of its actual value.
$$90\%\text{ of }X=\text{₹ }45,000$$
$$\frac{90}{100}\times X=45,000$$
$$X=\frac{45,000\times 100}{90}=\text{₹ }50,000$$
Thus, the actual revised value of the machinery that will appear in the new Balance Sheet is $\text{₹ }50,000$.