Selective maths: rates and work problems (8 questions)

Quick answer. A rate tells you how much is done in one unit of time. Write every rate in the same units, find the amount for one unit, then scale up or down. This page has two worked models and eight four-option questions in four pairs. Every solution line carries its units and ends with a sentence checking that the answer makes sense.

The Department of Education states that Mathematical Reasoning in the Selective High School Placement Test has 35 multiple-choice questions in 40 minutes, and that students cannot use a calculator in any section (Selective high school practice tests). This set is skill practice for Years 5 and 6. It does not claim that any item matches an official test question.

What is a rate?

A rate compares an amount with one unit of time: 6 litres per minute, 9 pages per minute, $14 per hour. Once you know the amount for one unit, any other amount of time is a multiplication or a division.

How do you keep the units consistent?

Before any arithmetic, read the units on every number and ask two things.

1. Is the rate per minute, per hour or per day?
2. Is the time asked for in the same unit? If not, change the time first (1 hour = 60 minutes; a quarter of an hour = 15 minutes).

Then write the unit after every number on every line. If a line has no unit, the working is not finished.

The eight questions

Choose the answer that fits. Work on paper; do not use a calculator.

Pair 1: find the amount for one unit, then scale

Question 1. A printer prints 45 pages in 5 minutes at a steady rate. How many pages does it print in 12 minutes?

A. 57 pages B. 108 pages C. 225 pages D. 540 pages

Question 2. Sam is paid $84 for 6 hours of work. Sam is paid the same amount for every hour. How much is Sam paid for 10 hours of work?

A. $94 B. $504 C. $140 D. $840

Pair 2: minutes against hours

Question 3. A machine fills 150 bottles every 10 minutes. How many bottles does it fill in 2 hours?

A. 300 bottles B. 1 800 bottles C. 900 bottles D. 18 000 bottles

Question 4. A hose delivers 24 litres of water in 3 minutes. How many litres does it deliver in a quarter of an hour?

A. 120 litres B. 39 litres C. 360 litres D. 480 litres

Pair 3: two machines working together

Question 5. Tap A fills a tank at 6 litres per minute. Tap B fills the same tank at 4 litres per minute. Both taps run together into the empty tank for 8 minutes. How many litres are in the tank?

A. 18 litres B. 48 litres C. 192 litres D. 80 litres

Question 6. Machine P packs 12 boxes per minute. Machine Q packs 90 boxes in 15 minutes. Working together, how many minutes do the two machines need to pack 180 boxes?

A. 15 minutes B. 30 minutes C. 10 minutes D. 2 minutes

Pair 4: more workers, less time

Question 7. 4 painters, each working at the same steady rate, paint a hall in 6 days. How many days do 8 painters need to paint the same hall?

A. 3 days B. 12 days C. 24 days D. 10 days

Question 8. 6 volunteers pack all the hampers for a charity in 10 hours, each working at the same steady rate. Only 4 volunteers are available. How many hours do 4 volunteers need to pack the same hampers?

A. 14 hours B. 60 hours C. 24 hours D. 15 hours

How is each one set out?

Model 1: a two-row table (unit rate)

A cleaner washes 18 windows in 3 hours at a steady rate. How many windows does the cleaner wash in 8 hours?

	Known	Wanted
Windows	18 windows	? windows
Hours	3 hours	8 hours

• Windows for 1 hour: 18 windows ÷ 3 hours = 6 windows per hour.
• Windows for 8 hours: 6 windows per hour × 8 hours = 48 windows.

Check. 8 hours is more than twice 3 hours and less than three times 3 hours, so the answer should be between 36 windows and 54 windows; 48 windows is in that range, which fits.

Table description for screen readers: two rows, windows and hours. The first column holds 18 windows and 3 hours. The second column holds an unknown number of windows and 8 hours.

Model 2: a labelled diagram (more workers, less time)

3 gardeners, each working at the same steady rate, plant a hedge in 8 hours. How many hours do 6 gardeners need?

Total work = 3 gardeners x 8 hours = 24 gardener-hours

  3 gardeners:  [ 8 hours ........................ ]
  6 gardeners:  [ ? hours ........ ]

Same total work:  6 gardeners x ? hours = 24 gardener-hours

• Total work: 3 gardeners × 8 hours = 24 gardener-hours.
• Time for 6 gardeners: 24 gardener-hours ÷ 6 gardeners = 4 hours.

Check. Twice as many gardeners should take half the time, and 4 hours is half of 8 hours.

Diagram description for screen readers: two horizontal bars. The top bar is labelled 3 gardeners and runs for 8 hours. The bottom bar is labelled 6 gardeners and is half as long, marked with a question mark for hours. Both bars represent the same total work of 24 gardener-hours.

Solutions

Question 1: B, 108 pages.

• Pages for 1 minute: 45 pages ÷ 5 minutes = 9 pages per minute.
• Pages for 12 minutes: 9 pages per minute × 12 minutes = 108 pages.

Check. 12 minutes is more than twice 5 minutes, so the answer must be more than 90 pages, and 108 pages is.

Question 2: C, $140.

• Pay for 1 hour: $84 ÷ 6 hours = $14 per hour.
• Pay for 10 hours: $14 per hour × 10 hours = $140.

Check. 10 hours is a little less than twice 6 hours, so the pay should be a little less than twice $84; $140 is under $168, so it fits.

Question 3: B, 1 800 bottles.

• Change the time first: 2 hours × 60 minutes per hour = 120 minutes.
• Bottles for 1 minute: 150 bottles ÷ 10 minutes = 15 bottles per minute.
• Bottles for 120 minutes: 15 bottles per minute × 120 minutes = 1 800 bottles.

Check. 120 minutes is 12 lots of 10 minutes, and 12 lots of 150 bottles is 1 800 bottles, which agrees.

Question 4: A, 120 litres.

• Change the time first: a quarter of an hour = 60 minutes ÷ 4 = 15 minutes.
• Litres for 1 minute: 24 litres ÷ 3 minutes = 8 litres per minute.
• Litres for 15 minutes: 8 litres per minute × 15 minutes = 120 litres.

Check. 15 minutes is 5 lots of 3 minutes, and 5 lots of 24 litres is 120 litres, which agrees.

Question 5: D, 80 litres.

• Combined rate: 6 litres per minute + 4 litres per minute = 10 litres per minute.
• Amount in 8 minutes: 10 litres per minute × 8 minutes = 80 litres.

Check. Tap A alone would give 48 litres in 8 minutes, and a second tap adds to it, so the total must be more than 48 litres.

Question 6: C, 10 minutes.

• Rate of Q: 90 boxes ÷ 15 minutes = 6 boxes per minute.
• Combined rate: 12 boxes per minute + 6 boxes per minute = 18 boxes per minute.
• Time for 180 boxes: 180 boxes ÷ 18 boxes per minute = 10 minutes.

Check. Machine P alone needs 15 minutes for 180 boxes, and adding a second machine must shorten that, so the answer must be under 15 minutes.

Question 7: A, 3 days.

• Total work: 4 painters × 6 days = 24 painter-days.
• Time for 8 painters: 24 painter-days ÷ 8 painters = 3 days.

Check. 8 painters is twice as many as 4 painters, so the job should take half of 6 days, which is 3 days.

Question 8: D, 15 hours.

• Total work: 6 volunteers × 10 hours = 60 volunteer-hours.
• Time for 4 volunteers: 60 volunteer-hours ÷ 4 volunteers = 15 hours.

Check. Fewer volunteers must take longer than 10 hours, and 15 hours is more than 10 hours.

Does the answer make sense?

Every solution above ends with a one-sentence check. Two quick ones work for most questions in this set.

• More of the cause, more of the result. More minutes, more taps or more machines gives a bigger total.
• More workers, less time. More workers on the same job gives a smaller number of hours or days; fewer workers gives a larger one.

If the answer goes the wrong way, the working has a slip in it.

What mistakes should we look for?

Question	Wrong option	What the child probably did
1	A, 57 pages	Added 12 to 45 instead of scaling the rate
1	C, 225 pages	Multiplied 45 pages by 5 minutes
2	A, $94	Added 10 to 84 instead of finding the hourly pay
3	A, 300 bottles	Multiplied 150 bottles by 2 hours and ignored the unit change
3	C, 900 bottles	Found the bottles for 1 hour, not 2 hours
3	D, 18 000 bottles	Multiplied 150 bottles by 120 minutes and forgot to divide by 10 minutes
4	B, 39 litres	Added 24 litres and 15 minutes instead of scaling the rate
4	C, 360 litres	Multiplied 24 litres by 15 minutes, treating a 3-minute amount as a 1-minute amount
4	D, 480 litres	Read a quarter of an hour as 60 minutes
5	A, 18 litres	Added 6, 4 and 8 together, mixing rates and time
5	B, 48 litres	Counted Tap A only
5	C, 192 litres	Multiplied 6, 4 and 8 together
6	A, 15 minutes	Used Machine P alone
6	B, 30 minutes	Used Machine Q alone
6	D, 2 minutes	Divided 180 boxes by 90 boxes and ignored the time
7	B, 12 days	Used direct proportion on an inverse situation
7	C, 24 days	Stopped one step early, at the 24 painter-days
7	D, 10 days	Added 4 to 6
8	A, 14 hours	Added 4 to 10
8	B, 60 hours	Stopped one step early, at the 60 volunteer-hours
8	C, 24 hours	Multiplied 6 volunteers by 4 volunteers

Can my child predict what changes?

Pick a solved question and change one number, then ask: "Will the answer go up or down? By roughly how much?" Only then calculate.

• Question 1 with 15 minutes instead of 12 minutes: up, by 3 minutes at 9 pages per minute.
• Question 5 with Tap B running at 2 litres per minute: down, because the combined rate drops from 10 litres per minute to 8 litres per minute.
• Question 7 with 12 painters instead of 8 painters: down, because more painters need fewer days.

What to do next

• Try a full set of questions in the free pack: free mock tests. A free account is needed to open the pack.
• Read the NSW Selective practice tests resources for how practice fits the wider preparation.
• Read the Selective Thinking Skills new format guide for the other half of the test.

Written by James Rush, Braintree Coaching Australia. Every answer was solved a second time without the answer key before publication. A named teacher review has not yet been recorded for this set, including whether combined rates suit Years 5-6. If you find an error, please tell us. Last updated 15 October 2026.