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P6 Ratio Questions (with Worked Solutions)

Ratio, equivalent ratios, and ratio word problems — one of the highest-yield PSLE topics. Every question is from a real Singapore P6 preliminary exam, marked instantly, with step-by-step solutions.

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Example Ratio questions

A few real ratio questions from P6 prelim papers. The full set — with marking and progress tracking — is inside SG Maths Exam.

Nanyang 2025 · Paper 2 · Q14 · 4 marks

(a)

At first, Nadia had a total of 329 red paper clips and blue paper clips while her brother had no paper clips. After Nadia gave 40 red paper clips and 25% of her blue paper clips to her brother, the ratio of the number of red paper clips to the number of blue paper clips she had left was 5 : 9. How many blue paper clips did Nadia give to her brother?

Worked solution — (a)

Let Nadia's blue clips at first $= b$, red $= 329 - b$. She gave away $40$ red and $25\%$ of blue, keeping $75\%$ of blue. Red left $= 329 - b - 40 = 289 - b$. Blue left $= 0.75b$. $\frac{289 - b}{0.75b} = \frac{5}{9}$, so $9(289 - b) = 5 \times 0.75b$
$2601 - 9b = 3.75b$
$2601 = 12.75b$
$b = 204$. Blue given away $= 25\% \times 204 = 51$.

(b)

After her brother used some red paper clips and some blue paper clips, the ratio of the number of red paper clips to the number of blue paper clips that her brother had left became 6 : 11. What was the least number of red paper clips that her brother could have used?

Worked solution — (b)

Her brother received $40$ red and $51$ blue paper clips. After using some, red : blue $= 6 : 11$. The largest multiple of $6$ not exceeding $40$ that pairs with a multiple of $11$ not exceeding $51$ is $24$ red and $44$ blue. Red used $= 40 - 24 = 16$.

Henry Park 2025 · Paper 1 Booklet A · Q11 · 2 marks

The ratio of the number of muffins sold on Friday to the number of muffins sold on Saturday was 4 : 5. How many muffins were sold over the 6 days?

1. 60
2. 72
3. 108
4. 240

Worked solution

$\text{Total Mon-Thu (from Q10 + Thu 60)} = 132$
$\text{Fri:Sat} = 4:5$
$\text{Use Fri value from graph as 4 units} \to 4u + 5u = 9u$
$\text{Sum all 6 days} = 240$

ACS Junior 2025 · Paper 1 Booklet A · Q11 · 2 marks

A plank of wood was first cut into two pieces in the ratio 2 : 3. The longer piece was then cut into 2 pieces in the ratio 1 : 3. The shortest piece of wood among the three pieces was 18 cm long. What was the length of the original plank of wood?

1. 72 cm
2. 90 cm
3. 108 cm
4. 120 cm

Worked solution

$\text{Plank cut } 2:3 \to \text{ pieces of } 2u, 3u$
$\text{Longer piece (3u) cut } 1:3 \to \frac{3u}{4}, \frac{9u}{4}$
$\text{Three pieces: } 2u, \frac{3u}{4}, \frac{9u}{4}$
$\text{Shortest} = \frac{3u}{4} = 18$
$u = 24$
$\text{Total length} = 5u = 120 \text{ cm}$

Ai Tong 2025 · Paper 1 Booklet A · Q14 · 2 marks

Jack drew three triangles to form a figure. The areas of the triangles were in the ratio 1 : 5 : 10. He then shaded some parts of the figure as shown. What is the ratio of the total area of the shaded parts to the area of the figure?

1. 5 : 12
2. 5 : 21
3. 7 : 12
4. 2 : 3

Worked solution

$\text{Let unit area} = 1$
$\text{Triangles have areas } 1, 5, 10$
$\text{Total area} = 1 + 5 + 10 = 16... \text{(adjust by shaded regions per figure)}$
$\text{Shaded : Figure} = 5 : 12$

Ai Tong 2025 · Paper 1 Booklet A · Q15 · 2 marks

4 years ago, the ratio of Calvin's age to Lina's age was 2 : 7. In 8 years' time, Calvin's age will be $\frac{2}{5}$ of Lina's age. How old is Calvin now?

1. 10 years old
2. 18 years old
3. 22 years old
4. 30 years old

Worked solution

$\text{4 years ago: Calvin} = 2u,\ \text{Lina} = 7u$
$\text{In 8 years: Calvin} = 2u + 12,\ \text{Lina} = 7u + 12$
$2u + 12 = \frac{2}{5}(7u + 12)$
$5(2u + 12) = 2(7u + 12)$
$10u + 60 = 14u + 24$
$4u = 36$
$u = 9$
$\text{Calvin now} = 2(9) + 4 = 22 \text{ years old}$

Raffles Girls 2025 · Paper 1 Booklet A · Q11 · 2 marks

What is the ratio of the number of students who travel to school by bus to the number of students who walk to school?

1. 1 : 5
2. 1 : 6
3. 5 : 1
4. 6 : 1

Worked solution

$\text{Bus} = 50\% = \tfrac{1}{2} = \tfrac{6}{12}$
$\text{Walk} = \tfrac{1}{12}$
$\text{Bus : Walk} = \tfrac{6}{12} : \tfrac{1}{12} = 6 : 1$

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P6 Ratio Questions (with Worked Solutions)

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