Existing Profit and Loss Account in the books of the firm will be shared/born by partners in the ratio:

The correct option is 5 : 3 : 2.

In partnership accounting, when a firm undergoes reconstitution (such as the admission of a new partner, retirement or death of an existing partner, or a change in the profit-sharing ratio), any existing accumulated profits or losses must be adjusted. The balance in the Profit and Loss Account represents accumulated profits (if it is a credit balance) or accumulated losses (if it is a debit balance) that were earned or incurred in the past.

Because these profits or losses relate to the period before reconstitution, they belong entirely to the existing partners in their old profit-sharing ratio. Therefore, the balance in the Profit and Loss Account is transferred to the partners' capital or current accounts in their old profit-sharing ratio, which in this case is 5 : 3 : 2.