In an activity based cost system; an activity/unit of work or task with differentiated purposes will be classified as

different task
purpose cost
an activity
an allocation cost

The correct answer is: C. an activity

An activity is a unit of work or task that is performed to achieve a specific objective. In an activity-based cost system, activities are classified according to their purpose. Activities with differentiated purposes are classified as different activities.

For example, in a manufacturing company, the activities of “machining” and “assembly” would be classified as different activities because they have different purposes. Machining is the process of shaping metal, while assembly is the process of putting together components to create a finished product.

Differentiating activities according to their purpose allows companies to more accurately allocate costs to products and services. This can lead to more accurate pricing and improved profitability.

Option A is incorrect because a different task is not necessarily an activity. A task is a unit of work that is performed to achieve a specific objective, but it may not be an activity if it does not have a specific purpose.

Option B is incorrect because a purpose cost is a cost that is incurred to achieve a specific objective. This type of cost is not necessarily associated with an activity.

Option D is incorrect because an allocation cost is a cost that is assigned to a product or service based on an arbitrary or indirect method. This type of cost is not necessarily associated with an activity.