Victorian selective entry: 10 ratio problems in context

Quick Answer

For Victorian selective entry maths practice, find what one part is worth, then scale. When a second condition changes the ratio, rebuild the parts from the new information instead of adjusting the old answer. This page from Braintree Coaching Australia has ten original ratio problems for Year 8 students (three sharing, three two-stage, two comparison, two combined-ratio), each with a bar-model solution. It is free and needs no sign-up.

Who are these ratio problems for?

These suit a Year 8 student in Victoria preparing for selective entry to Year 9 who can already share an amount in a ratio and now needs to handle problems where the ratio changes or two ratios meet. The Victorian Government says candidates sit the exam in Year 8 for Year 9 entry (selective entry high schools, read 2026-10-15). The set is skill practice. It is not made of official questions and we do not say it matches exam difficulty.

"SEHS" is also an abbreviation used for other things online. Here we mean the Victorian selective entry high schools exam run by ACER.

Where do ratios sit in the Victorian selective entry exam?

ACER's preparation page says Mathematics "assesses year-level appropriate mathematical knowledge and reasoning" and Quantitative Reasoning "assesses the ability to think and reason using numbers, patterns, and shapes". It also says the required knowledge in any section will not exceed the Year 8 curriculum. It does not mention ratio or proportion, so ACER does not say which section ratio questions fall in. We label this page as mathematics practice and leave it there.

On the day, Mathematics and Quantitative Reasoning share one 60-minute block, and ACER's exam day page lists calculators as not permitted. Our exam format guide covers the other blocks, and the practice resources guide explains where this set fits.

How do we solve a two-stage ratio problem? Two worked models

Model 1: sharing. Tea and milk are mixed in the ratio 2 : 5 to make 63 mL. How much milk?

tea   | 2 parts |
milk  | 5 parts |        7 parts = 63 mL
one part = 63 ÷ 7 = 9 mL      milk = 5 × 9 = 45 mL

Model 2: two-stage. Red and blue counters are in the ratio 3 : 2. After 10 red counters are removed the ratio is 1 : 2. How many counters were there at first?

The blue counters do not change, so keep them as the fixed bar and rebuild the red bar from the new ratio.

before   red  | 3 parts |        blue | 2 parts |
after    red  | 1 part  |        blue | 2 parts |   (blue unchanged)
red lost = 3 − 1 = 2 parts = 10 counters, so one part = 5
at first: 5 parts × 5 = 25 counters

The trap is to subtract 10 from both sides or to keep the old part value. Rebuild the bars from the new ratio, matching the quantity that did not change.

The questions

Choose the one correct option. Draw the bar before you look at the options, and no calculator.

Question 1. Mia and Leo share $240 in the ratio 3 : 5. How much does Leo get?

• A. $90
• B. $150
• C. $48
• D. $80

Question 2. Ava, Ben and Cara share 72 stickers in the ratio 2 : 3 : 4. How many more stickers does Cara get than Ava?

• A. 8
• B. 24
• C. 32
• D. 16

Question 3. A bag has red and blue marbles in the ratio 4 : 7. There are 36 more blue marbles than red. How many marbles are in the bag?

• A. 48
• B. 84
• C. 132
• D. 396

Question 4. A camp has boys and girls in the ratio 5 : 3. After 12 more girls arrive there are the same number of boys and girls. How many students were at the camp at first?

• A. 48
• B. 8
• C. 30
• D. 60

Question 5. A jar has orange and lemon lollies in the ratio 7 : 4. After 20 orange lollies are eaten the ratio of orange to lemon is 1 : 2. How many lemon lollies are in the jar?

• A. 8
• B. 16
• C. 20
• D. 28

Question 6. Pam and Raj have money in the ratio 4 : 3. Pam spends $18 and Raj spends nothing. Then the ratio of Pam's money to Raj's is 2 : 3. How much money did they have altogether at first?

• A. $27
• B. $36
• C. $45
• D. $63

Question 7. Glass P is made with 1 part cordial to 4 parts water. Glass Q is made with 2 parts cordial to 7 parts water. Which statement is true?

• A. P is stronger, because it uses 4 parts of water to each part of cordial.
• B. P is stronger, because 1 out of 5 parts is more than 2 out of 9 parts.
• C. Q is stronger, because it has 3½ parts of water to each part of cordial, fewer than P's 4.
• D. They are equally strong, because both have more than three times as much water as cordial.

Question 8. Mia mixes blue and yellow paint in the ratio 3 : 2. Noah mixes them in the ratio 5 : 4. Each uses 20 mL of yellow. How many mL more blue does Mia use than Noah?

• A. 5
• B. 10
• C. 15
• D. 30

Question 9. The ratio of a to b is 2 : 3 and the ratio of b to c is 4 : 5. What is the ratio of a to c?

• A. 2 : 5
• B. 8 : 15
• C. 3 : 4
• D. 5 : 6

Question 10. The ratio of Ali's savings to Ben's is 3 : 4. The ratio of Ben's savings to Cal's is 6 : 7. Together they have $175. How much does Cal have?

• A. $45
• B. $60
• C. $100
• D. $70

Answers and complete solutions

Question 1: B, $150 (sharing). 3 + 5 = 8 parts, so one part is 240 ÷ 8 = $30 and Leo's 5 parts are $150. A is Mia's share. C divides by 5. D divides by 3.

Mia  | 3 | 
Leo  | 5 |      8 parts = $240, one part = $30, Leo = 5 × 30

Question 2: D, 16 (sharing). 2 + 3 + 4 = 9 parts, so one part is 72 ÷ 9 = 8. Cara has 4 × 8 = 32 and Ava 2 × 8 = 16. The difference is 2 parts, 16 stickers. A is one part, B is Ben's share and C is Cara's share, not the difference.

Question 3: C, 132 (sharing with a difference). The bars differ by 7 − 4 = 3 parts, which is 36 marbles, so one part is 12. The total is 11 parts, 11 × 12 = 132. A is the red marbles, B the blue, D multiplies the difference by 11.

red   | 4 |
blue  | 4 | 3 |     3 parts = 36, one part = 12, total 11 parts = 132

Question 4: A, 48 (two-stage). The boys do not change, so they stay at 5 parts. The girls grow from 3 parts to 5 parts, so 2 parts is 12 students, and one part is 6. At first there were 8 parts, 8 × 6 = 48. B is the number of parts, C is the number of boys and D is the total after the girls arrive.

Question 5: B, 16 (two-stage). The lemon lollies do not change: 4 parts. After the change orange is half of lemon, 2 parts. Orange lost 7 − 2 = 5 parts = 20 lollies, so one part is 4 and lemon is 4 × 4 = 16. A is the orange left, C is the number eaten and D is the original orange count. The trap is subtracting 20 from both sides.

before  orange | 7 parts |   lemon | 4 parts |
after   orange | 2 parts |   lemon | 4 parts |    5 parts = 20, part = 4

Question 6: D, $63 (two-stage). Raj's money does not change: 3 parts. After spending Pam has 2 of those same parts, so she spent 4 − 2 = 2 parts = $18 and one part is $9. They had 7 parts, 7 × 9 = $63. A is Raj's money, B is Pam's, and C is the total after Pam spends ($18 + $27).

Question 7: C (comparison). Compare the same measure in both glasses: water for each part of cordial. P has 4 and Q has 7 ÷ 2 = 3½. Less water for each part of cordial means stronger, so Q is stronger. As fractions, P is 1/5 = 0.2 cordial and Q is 2/9, about 0.22. B has the comparison the wrong way round. A and D do not compare like with like.

Question 8: A, 5 (comparison). Scale each ratio to 20 mL of yellow. Mia: 2 parts = 20, one part 10, blue 3 × 10 = 30 mL. Noah: 4 parts = 20, one part 5, blue 5 × 5 = 25 mL. Mia uses 5 mL more. B is Mia's part value and D is Mia's blue. The trap is comparing 3 with 5 without scaling.

Question 9: B, 8 : 15 (combined ratio). The shared term b must match. In a : b = 2 : 3 and b : c = 4 : 5, make b equal 12 in both: a : b = 8 : 12 and b : c = 12 : 15. So a : b : c = 8 : 12 : 15 and a : c = 8 : 15. A takes the outer numbers. C joins the two middle numbers. D multiplies across the ratios (2 × 5 : 3 × 4 = 10 : 12 = 5 : 6).

a | 8  |
b | 12 |            a : b : c = 8 : 12 : 15
c | 15 |

Question 10: D, $70 (combined ratio). Make Ben's term match: 3 : 4 becomes 9 : 12 (× 3) and 6 : 7 becomes 12 : 14 (× 2). So Ali : Ben : Cal = 9 : 12 : 14, which is 35 parts = $175, one part is $5. Cal has 14 × 5 = $70. A is Ali's amount, B is Ben's, and C takes 4/7 of the total.

What mistake patterns should we look for?

Tally which wrong option your child chose. Each needs a different fix.

Pattern	Seen in	What to practise next
Part-to-part read as part-to-whole, or the wrong number of parts used	Questions 1C, 1D, 2A, 3A, 3B, 4B	Write "total parts = ?" before dividing
Adding or subtracting the same amount from both parts instead of rebuilding the bars	Questions 4C, 4D, 5C, 5D, 6C	Circle the quantity that does not change and keep that bar fixed
Comparing the numbers in two ratios without making them like for like	Questions 7A, 7B, 7D, 8B, 8D	Scale both to the same amount of one part before comparing
Combining ratios without matching the shared term	Questions 9A, 9C, 9D, 10A, 10B, 10C	Rewrite both ratios so the shared quantity has the same number

Can my child write a ratio from a new situation?

A recipe uses 300 g of flour for every 200 g of sugar. A map has a scale of 1 : 50 000, and two towns are 4 cm apart on the map. Write each as a ratio, then make up one two-stage question of your own and solve it with a bar.

Self-check: the recipe is 3 : 2 (or 300 : 200). On the map, 4 cm stands for 4 × 50 000 = 200 000 cm, which is 2 km. A good question changes one quantity, keeps the other fixed, and has a whole-number answer.

What should we do after this set?

• If most errors were rebuilding errors, redo Questions 4, 5 and 6 tomorrow and name the unchanged quantity before drawing.
• For official-format practice see ACER's preparation page and our Victorian practice resources guide.
• Our free SEHS sample questions cover mixed skills, and the free mock tests need a free classroom account.
• If you want a structured programme after that, see what the Victorian SEHS course includes and check it matches your child's entry year before buying.

Sources and review

Official sources (read 2026-10-15): ACER, Prepare for the exam: the component definitions above, the Year 8 curriculum ceiling, no mention of ratio. ACER, Exam day: the 60-minute Mathematics and Quantitative Reasoning block and calculators not permitted. Victorian Government, Selective entry high schools: sat in Year 8 for Year 9 entry.

Where the questions came from: all ten problems, the worked models and the transfer task are original Braintree Coaching Australia material written for this page. The names and quantities are made up. None is taken from an official or third-party paper.

Author: James Rush, content writer, Braintree Coaching Australia.

Answer check: on 2026-10-15 every answer was recomputed and every wrong option checked by a second pass that had the key in front of it, so it tests the arithmetic and the wording, not a cold solve. A blind solve by someone who has not seen the keys and a named teacher review have not yet been recorded for this set. If you find an error, please tell us.

Last updated: 2026-10-15.