PSLE Mathematics · Primary 5 and 6
PSLE Math Rate: Amount per Unit Questions Explained
By The Singapore Syllabus · Updated · How this guide is checked
Quick answer
A rate is the amount of one quantity for each unit of another quantity, such as 12 litres per minute. Rate = total amount ÷ number of units. Total amount = rate × number of units. Number of units = total amount ÷ rate. Write every rate with both of its units, such as ℓ/min or $ per hour, so you can see which quantity is per which.
- Rate = total amount ÷ number of units.
- Total amount = rate × number of units.
- Number of units = total amount ÷ rate.
- Read 'per' as 'for each': 12 ℓ per min means 12 litres every minute.
Rate in PSLE Math is the amount of one quantity per unit of another quantity, such as 12 litres per minute or $15 per hour. It is a Primary 5 topic, and every question asks for one of three things: the rate, the total amount or the number of units, given the other two. The usual confusion is which quantity goes first, litres per minute or minutes per litre. Speed, distance and time questions are not in the 2021 primary syllabus and are taught in secondary school.
What does the syllabus expect for Rate?
Where it sits: MOE 2021 Primary Mathematics, Number and Algebra, Rate (P5).
- Understand rate as the amount of a quantity per unit of another quantity (P5)
- Find the rate given the total amount and the number of units (P5)
- Find the total amount given the rate and the number of units (P5)
- Find the number of units given the rate and the total amount (P5)
What is a rate?
A rate is the amount of one quantity for each unit of another quantity. A tap that fills 12 litres of water every minute has a rate of 12 litres per minute, written 12 ℓ/min. A worker paid $15 for every hour has a rate of $15 per hour, and a printer that prints 30 pages every minute has a rate of 30 pages per minute. The word 'per' means 'for each', and the quantity after 'per' is the unit you count in.
A rate always has two units, one before 'per' and one after it, so the units are part of the answer. 12 ℓ/min and 12 min/ℓ are very different: the first is a fast tap, while the second is a slow one that needs 12 minutes for each litre. Before calculating, say the rate aloud as 'so much for each one', for example '12 litres for each minute'.
How do you find the rate?
To find the rate, divide the total amount by the number of units, so rate = total amount ÷ number of units. A printer that prints 450 pages in 15 minutes has a rate of 450 ÷ 15 = 30 pages per minute. If 6 kg of rice costs $9, the rate is $9 ÷ 6 = $1.50 per kg.
The number of units must be in the unit the rate is asked for. If a tap fills 90 litres in 2 hours and the question wants litres per minute, change 2 hours into 120 minutes first, so the rate is 90 ÷ 120 = 0.75 ℓ/min, which is 750 ml per minute. Dividing the other way round, 120 ÷ 90, gives minutes per litre, which answers a different question.
How do you find the total amount or the number of units?
To find the total amount, multiply the rate by the number of units, so total amount = rate × number of units. A worker paid $15 per hour earns $15 × 8 = $120 in 8 hours. A tap filling 12 ℓ/min puts 12 × 25 = 300 litres into a tank in 25 minutes.
To find the number of units, divide the total amount by the rate, so number of units = total amount ÷ rate. A 300-litre tank filled at 12 ℓ/min takes 300 ÷ 12 = 25 minutes. A worker earning $15 per hour needs $180 ÷ $15 = 12 hours to earn $180. To check any rate answer, put it back into rate × number of units and see whether it gives the total amount.
How do you solve questions with two rates?
Questions with two rates are solved by using rate × number of units for each part, then combining the parts. A plumber charges $40 per hour for the first 2 hours and $25 per hour after that. A 5-hour job costs 2 × $40 = $80 for the first part and 3 × $25 = $75 for the rest, so $155 altogether. When two taps run together, their rates add: taps filling 8 ℓ/min and 12 ℓ/min together fill 20 litres every minute, so a 300-litre tank fills in 300 ÷ 20 = 15 minutes.
When a rate stays the same, the total amount goes up by the same step for every unit. A table of minutes against litres for a 12 ℓ/min tap reads 12, 24, 36 and so on, and a line graph of it is a straight line starting at 0. A steeper line means a higher rate.
| To find | Formula | Example |
|---|---|---|
| Rate | Total amount ÷ number of units | 300 ℓ in 25 min gives 12 ℓ/min |
| Total amount | Rate × number of units | 12 ℓ/min for 25 min gives 300 ℓ |
| Number of units | Total amount ÷ rate | 300 ℓ at 12 ℓ/min takes 25 min |
| Rate | Read it as | Total for 6 units |
|---|---|---|
| 12 ℓ/min | 12 litres for each minute | 72 ℓ in 6 min |
| $15 per hour | $15 for each hour | $90 for 6 hours |
| 30 pages per minute | 30 pages for each minute | 180 pages in 6 min |
| $1.50 per kg | $1.50 for each kilogram | $9 for 6 kg |
Worked example
How do you answer an exam question on Rate?
An empty tank holds 300 litres. Tap A fills it at 12 litres per minute. (a) How long does Tap A alone take to fill the tank? (b) Instead, Tap A runs alone for 10 minutes, and then Tap B, which fills at 8 litres per minute, is also turned on. How many more minutes are needed to fill the tank?
- (a) Number of units = total amount ÷ rate = 300 ÷ 12 = 25 minutes.
- (b) In the first 10 minutes Tap A puts in 12 × 10 = 120 litres.
- Water still needed = 300 − 120 = 180 litres.
- With both taps on, the rates add: 12 + 8 = 20 litres every minute.
- Time needed = 180 ÷ 20 = 9 minutes.
- Check: Tap A runs 10 + 9 = 19 minutes and gives 12 × 19 = 228 litres. Tap B runs 9 minutes and gives 8 × 9 = 72 litres. 228 + 72 = 300 litres.
Answer: (a) 25 minutes (b) 9 more minutes
Which mistakes lose marks in Rate?
- Dividing the wrong way round. For 90 litres in 120 minutes, 120 ÷ 90 gives minutes per litre. Put the quantity before 'per' on top: 90 ÷ 120 = 0.75 ℓ/min.
- Mixing units of time. A tap at 12 ℓ/min running for 1 1/2 hours runs for 90 minutes, so it fills 12 × 90 = 1080 litres, not 12 × 1.5 = 18 litres.
- Using one tap's rate after a second tap is turned on. From that moment both taps fill together, so use 12 + 8 = 20 ℓ/min.
- Keeping one rate for a whole job when the question changes it, such as $40 per hour for the first 2 hours and $25 per hour after that. Split the job into parts.
- Leaving the units off a rate, such as writing 30 instead of 30 pages per minute. A rate needs both of its units.
- Writing a money rate as $1.5 per kg instead of $1.50 per kg. Money is written to 2 decimal places.
How do you score well on Rate questions?
- Write each rate with both units, such as 12 ℓ/min, and check that the units in your multiplication or division match them.
- Change times into the unit of the rate before calculating, for example 1 1/2 h into 90 min for a rate in litres per minute.
- When a rate changes or a second tap is turned on, split the time into parts and use rate × number of units for each part.
Practice questions
1. Easy: A printer prints 270 pages in 9 minutes. What is its rate in pages per minute?
Show answer
30 pages per minute. Working: rate = total amount ÷ number of units = 270 ÷ 9 = 30.
2. Medium: Mr Tan is paid $18 per hour. How many hours must he work to earn $414?
Show answer
23 hours. Working: number of units = total amount ÷ rate = 414 ÷ 18 = 23. Check: 18 × 23 = 414.
3. Harder: An empty rectangular tank measures 60 cm by 50 cm by 40 cm (height). A tap fills it at 15 litres per minute. How long does the tap take to fill the tank to a height of 30 cm?
Show answer
6 minutes. Working: volume of water needed = 60 × 50 × 30 = 90 000 cm³ = 90 ℓ. Time = 90 ÷ 15 = 6 minutes. Check: 15 × 6 = 90 ℓ.
Questions students and parents ask
What does rate mean in PSLE Math?
A rate is the amount of one quantity for each unit of another quantity, such as 12 litres per minute or $15 per hour. Rate questions give two of the rate, the total amount and the number of units, and ask for the third.
How do you find the number of units from a rate?
Divide the total amount by the rate. A 300-litre tank filled at 12 litres per minute takes 300 ÷ 12 = 25 minutes. Check by multiplying back: 12 × 25 = 300.
What happens to the rate when two taps fill a tank together?
The rates add. Taps filling 12 litres per minute and 8 litres per minute together fill 20 litres every minute, so 180 litres takes 180 ÷ 20 = 9 minutes.
Related topics
- Volume of Cubes and Cuboids. Next: tank filling questions combine a rate with litres and cm³.
- Decimals. Rates such as $1.50 per kg and 0.75 ℓ/min need decimal division.
- Ratio. Rate, like ratio, compares two quantities that change in proportion.
- Average. Average and rate both divide a total by a number of units.
- All PSLE Mathematics topics
Official syllabus
This guide follows the syllabus documents published by the Singapore Examinations and Assessment Board.
- MOE, 2021 Primary Mathematics syllabus (Primary 1 to 6)
- SEAB, PSLE Mathematics exam format 0008 (2026)
First published 16 October 2026. Updated 17 October 2026 with the quick answer, tables, diagram and FAQs. Every worked example and practice answer on this page was checked a second time, separately from the writing, before publishing. Spotted an error? Tell us and we will correct it.
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