I have seen more "profits". But I am confused about when to go for plural. Is this case, which is better?
I was, in a past life, a practising Chartered Accountant. The terms "profit and loss" and "profits and losses" are near and dear to me.
The term "profit and loss", or an organisation's "responsibility for its profit and loss", is a general reference to that organisation's obligation to prepare its own financial statements.
The term "profits and losses" refers to the results from trading, and the expectation that the managers of a business or organisation will be held accountable for those results.
Historically, the profit and loss statement (or "profit and loss") is regarded as one of two essential documents that enable persons to assess the financial performance of an organisation. Together with the balance sheet, they are known as "the accounts", and they are prepared regularly and consistently from the accounting systems. There are also other regular financial calculations and disclosures that are prepared but normally everything is grouped under the generic heading of "the accounts". So the term "profit and loss", or an organisation's "responsibility for its profit and loss", is a general reference to the accounts, and an organisation's obligation to prepare its own financial statements.
An organisation will enter into many transactions over a day, week, month, or year. The managers of that organisation must have systems that enable them to calculate or predict whether each and every one of those transactions will produce a profit or a loss. For a variety of reasons, some transactions may deliberately yield a profit and others may generate a loss; profits and/or losses may be large or small, individually and/or collectively. The common theme, however, is that the organisation's management should be able to predict the level of profit and loss on each transaction. So when one hears that an organisation is "responsible for its profits & losses", one understands that the managers of the organisation are responsible for the organisation's trading decisions and outcomes.
Generally, you use profit to describe the result of one particular transaction (one sale). For an entire department, you'd want to summarize the results of multiple transaction over some time period as their profits, plural.
Both options are correct, but the plural option sounds more natural and is more formal.
