Sec 1 Maths · Ratio, rate and speed

Rates questions with answers

Practice questions on rates, from the basics up to exam level, each with a full worked solution. Try them on paper first, then open the solution to check your working.

Worked example

A hawker sells 120 plates of chicken rice in 5 hours. Find the rate, in plates per hour.

Step 1 of 1

Find the rate: multiply or divide?

\text{Rate} = \dfrac{120}{5}

= 24

The rate is

24

plates per hour.

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Questions

Question 1Find a rate
A tap fills a tank with 120 litres of water in 15 minutes. Find the rate of flow, in litres per minute.
Show the worked solution
1. Step 1: Find the rate: multiply or divide? $\text{Rate} = \dfrac{120}{15}$ $= 8$ The rate is $8$ litres per minute.
Question 2Use a rate to find an amount
A hawker sells 35 plates of chicken rice per hour. Find the number of plates she sells in 8 hours.
Show the worked solution
1. Step 1: Use the rate: multiply or divide? $35 \times 8$ $= 280$ $280$ plates
Question 3Use a rate to find the time
A printer prints 20 pages per minute. Find the time, in minutes, it takes to print 120 pages.
Show the worked solution
1. Step 1: Find the number of minutes: multiply or divide? $\dfrac{120}{20}$ $= 6$ $6$ minutes
Question 4Best buy
The table shows the sizes and prices of two packets of shampoo. Which packet is the best buy?
Packet A B
Volume 200 ml 500 ml
Price $1.60 $3.75
Show the worked solution
1. Step 1: Find the price of 100 ml in each packet (in dollars) $\text{A: } \dfrac{1.60}{200} \times 100 = 0.8$ $\text{B: } \dfrac{3.75}{500} \times 100 = 0.75$
2. Step 2: The best buy costs the least for the same amountPacket B costs the least for 100 ml ($0.75), so it is the best buy.
Question 5Rates with a change of unit
A car uses 8 litres of petrol for every 100 km. Find the volume of petrol, in litres, it uses for a journey of 350 km.
Show the worked solution
1. Step 1: How many lots of 100 km? $\dfrac{350}{100} = 3.5$
2. Step 2: Multiply by the petrol used for each 100 km $8 \times 3.5 = 28 \text{ litres}$
Question 6Scale a recipe, whole packets, a bulk offer
A recipe uses 450 g of flour to make one loaf of bread. A baker makes 15 loaves of bread. Flour is sold in 2 kg packets at $4.20 each, and the shop has an offer: every second packet is 30% off. Find the least amount the baker pays for the flour needed.
Show the worked solution
1. Step 1: Flour needed: scale the recipe (in grams) $\dfrac{450}{1} \times 15 = 6750 \text{ g}$
2. Step 2: Packets to buy: divide, then round UP (a part packet can't be bought) $\dfrac{6750}{2000} = 3.375, \text{ so } 4 \text{ packets}$
3. Step 3: The offer: in each pair of packets, the second is cheaper (in dollars) $\text{Second packet} = \dfrac{70}{100} \times 4.2$ $\phantom{\text{Second packet}} = 2.94$ $2 \times (4.2 + 2.94) = 14.28$ The baker pays $14.28.

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Questions

Question 1Find a rate

A tap fills a tank with 120 litres of water in 15 minutes. Find the rate of flow, in litres per minute.

Show the worked solution

Step 1: Find the rate: multiply or divide? $\text{Rate} = \dfrac{120}{15}$ $= 8$ The rate is $8$ litres per minute.

Question 2Use a rate to find an amount

A hawker sells 35 plates of chicken rice per hour. Find the number of plates she sells in 8 hours.

Show the worked solution

Step 1: Use the rate: multiply or divide? $35 \times 8$ $= 280$ $280$ plates

Question 3Use a rate to find the time

A printer prints 20 pages per minute. Find the time, in minutes, it takes to print 120 pages.

Show the worked solution

Step 1: Find the number of minutes: multiply or divide? $\dfrac{120}{20}$ $= 6$ $6$ minutes

Question 4Best buy

The table shows the sizes and prices of two packets of shampoo. Which packet is the best buy?

Packet	A	B
Volume	200 ml	500 ml
Price	$1.60	$3.75

Show the worked solution

Step 1: Find the price of 100 ml in each packet (in dollars) $\text{A: } \dfrac{1.60}{200} \times 100 = 0.8$ $\text{B: } \dfrac{3.75}{500} \times 100 = 0.75$
Step 2: The best buy costs the least for the same amountPacket B costs the least for 100 ml ($0.75), so it is the best buy.

Question 5Rates with a change of unit

A car uses 8 litres of petrol for every 100 km. Find the volume of petrol, in litres, it uses for a journey of 350 km.

Show the worked solution

Step 1: How many lots of 100 km? $\dfrac{350}{100} = 3.5$
Step 2: Multiply by the petrol used for each 100 km $8 \times 3.5 = 28 \text{ litres}$

Question 6Scale a recipe, whole packets, a bulk offer

A recipe uses 450 g of flour to make one loaf of bread. A baker makes 15 loaves of bread. Flour is sold in 2 kg packets at $4.20 each, and the shop has an offer: every second packet is 30% off. Find the least amount the baker pays for the flour needed.

Show the worked solution

Step 1: Flour needed: scale the recipe (in grams) $\dfrac{450}{1} \times 15 = 6750 \text{ g}$
Step 2: Packets to buy: divide, then round UP (a part packet can't be bought) $\dfrac{6750}{2000} = 3.375, \text{ so } 4 \text{ packets}$
Step 3: The offer: in each pair of packets, the second is cheaper (in dollars) $\text{Second packet} = \dfrac{70}{100} \times 4.2$ $\phantom{\text{Second packet}} = 2.94$ $2 \times (4.2 + 2.94) = 14.28$ The baker pays $14.28.