The term “pure profit” is generally used to mean something very similar to economic profit.
Economic profit takes into account both explicit cost and implicit cost. Explicit costs are those that are actually paid out to other people. Implicit costs are the opportunity costs incurred by the owner of the business. For example, if that owner quits his or her job to start a new company, the pay they got at the old job would be part of the implicit costs because the owner is foregoing that in order to start the new company.
Pure profit, then, refers to what is left over after all conceivable costs (including implicit costs) are subtracted from gross revenue.
When talking about profits most of the time what is being referred to is accounting profit or basically the revenues less explicit costs. Explicit costs may include salaries, transportation and utilities. On the other hand, pure profit or economic profit is profit that is determined by capturing the explicit and implicit costs or what are generally known as opportunity costs. Implicit costs are costs that are incurred by forgoing different gains during operations. For instance, a company’s own building may be rented out to generate income but since it is alternatively being used as a warehouse then the forgone rent becomes an economic cost to the business. Pure profit is thus the deduction of both explicit and implicit costs from total revenues. It is also important to note that accounting profits are determined based on Generally Accepted Accounting Principles (GAAP) while pure profits are determined based on economic principles which factor in all types of costs and earnings.
It is highly unlikely that the business registered $75,000 as pure profit; this is because bank statements are based on reported earnings which always conform to GAAP standards. In that case if the reported $75,000 bank balance is considered profit then it is accounting profit and not pure profit.
Pure Profit or economic profit is different from accounting profit (or what we normally understand as profit). Accounting profit is the difference between total revenue and total direct costs (such as wages, rent, cost of materials, interest, etc.).
i.e. accounting profit = total revenue - (interest + wages+ rent + material cost)
Pure profit or economic profit also accounts for implicit costs such as opportunity cost, insurable risks, depreciation and necessary minimum payment to stock holders to prevent them from withdrawing their capital. Opportunity cost refers to the opportunity forgone in order to pursue the current occupation. For example, the regular salary that a person will have to forgo in order to pursue the current profession or amount of interest forgone on self-capital invested, etc.
i.e. pure profit = accounting profit- implicit cost
From the data you have provided (initial bank balance and the same at a later date), without making assumptions (such as no other transaction from that account except for business, implicit cost, etc.) we cannot determine pure profit. Although it would seem that the venture made $75,000 - $ 3000 = $72,000 in the given duration. And it is pure profit, given that implicit cost is not given.