Per unit and rate questions

Numerical reasoning practice > Per unit and rate questions

A rate is one quantity divided by another. These questions are easy arithmetic wrapped in wording designed to make you divide the wrong way round.

1. Which way to divide

The unit of the answer tells you the division. Read the unit in the question before anything else.

• Price per unit is pounds per item, so pounds ÷ items
• Units per employee is items per person, so items ÷ people
• Revenue per square metre is pounds ÷ area

"Per" always means "divided by the thing that follows". If you can say the unit out loud, you have the formula.

2. Worked example: average price per unit

The table below shows the number of units sold and the revenue for each product.

Product C 1,250 units / £7,500
Product A 950 units / £11,400
Product D 1,400 units / £19,600
Product B 1,500 units / £9,000

What is the average price per unit for Product C?

How to work it

• Price per unit is pounds ÷ items
• Only the Product C row matters: 7,500 ÷ 1,250
• 7,500 ÷ 1,250 = £6

Three of the four rows are there to see whether you read the row name. This is the same skipping skill as a table question.

3. You cannot average an average

If Product C sells at £6 per unit and Product A at £12, the average price across both is not £9 unless they sold the same number of units.

• Add the revenues: 7,500 + 11,400 = 18,900
• Add the units: 1,250 + 950 = 2,200
• Divide once: 18,900 ÷ 2,200 ≈ £8.59

This is a weighted average, and the unweighted answer (£9.00) is always offered as an option.

4. Sense-checking the answer

Rates have an intuitive size. Before you commit:

• A price per unit should look like a price. £6 is plausible; £6,000 for a retail item is not
• If you divided the wrong way you get the reciprocal, which is usually absurdly small (0.167) or absurdly large
• One glance at whether the number is believable catches most inversion errors