Bus operator numeracy practice: units, percentages and averages

Write the question as a quantity

Before calculating, finish the sentence “I need the number of ___.” That might be passengers remaining, dollars collected, minutes late or passengers per trip. This small step prevents a correct calculation from answering the wrong question. Keep a unit beside your answer rather than leaving an unexplained number.

These exercises practise arithmetic using invented figures. They do not state a vehicle capacity, fare policy, loading procedure or employer test syllabus. If your assessment supplies a rounding instruction or calculator restriction, use that instruction instead of assuming one from this article.

Example 1: follow a passenger count in order

A fictional bus has 18 passengers. At the next stop, seven leave and eleven board. There are 18 − 7 + 11 = 22 passengers afterward. At a second stop, five leave and two board, leaving 19. The first change is a net increase of four; the second is a net decrease of three.

Check by combining all changes: 18 − 7 + 11 − 5 + 2 = 19. If you add everyone who boarded, 13, you have answered a different question. If you add the two intermediate totals, you have counted some passengers more than once. Label each running total with the stop it belongs to.

Example 2: calculate a percentage increase

A practice table records 80 journeys on one day and 100 on another. The increase is 20 journeys. Divide that change by the original 80, then multiply by 100: 20 ÷ 80 × 100 = 25%. Dividing by 100 would instead compare the change with the later value.

Now reverse the journey. A fall from 100 to 80 is a 20% decrease because the starting value is 100. The same absolute difference does not produce the same percentage in both directions. Always name the starting point before choosing a denominator.

Example 3: distinguish a total from an average

Three fictional trips carry 12, 18 and 24 boardings. The total is 54 boardings and the arithmetic mean is 54 ÷ 3 = 18 boardings per trip. A fourth trip with six boardings changes the total to 60 and the mean to 60 ÷ 4 = 15.

Do not average the old mean, 18, and the new observation, six, to get 12. That would give the single new trip the same weight as the earlier group of three. Rebuild the total and divide by all four observations. This habit is useful whenever a question adds data to an existing summary.

Example 4: keep money units consistent

In a fictional exercise, six tickets cost $2.75 each. The total is $16.50. You can multiply 275 cents by six to get 1,650 cents, then divide by 100 to return to dollars. A practice payment of $20.00 leaves a numerical difference of $3.50.

This is a money calculation, not a claim that an operator sells these tickets or gives change. Follow the supplied question and keep real agency payment procedures separate. If your result is $165.00, a rough check—six amounts just under $3—shows the decimal has moved incorrectly.

Review the reason for each answer

Try each example again with new numbers. Before checking, say why you added, subtracted, multiplied or divided. Then inspect the unit, base value and number of observations. Record recurring errors in your practice journal and combine arithmetic with timetable questions when the separate methods are clear.

Common questions

Original TransitPrep practice material. All example figures, networks, notices and procedures on this page are fictional. They do not reproduce an employer’s examination.