Final answer:
When a new partner is admitted into a partnership and the capital of the old partners decreases, it is due to the write-up of undervalued assets to their fair values.
Step-by-step explanation:
When a new partner is admitted into a partnership and the capital of the old partners decreases, the reason for the decrease is the write-up of undervalued assets to their fair values.
This means that the previously undervalued assets are now recognized at their actual market values, resulting in an increase in the partnership's capital.
The decrease in the capital of the old partners reflects the redistribution of ownership and profits among the partners.