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P6 Ratio Questions (with Worked 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(a) · 3 marks

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

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 $= 25\% \times 204 = 51$.

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 · 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 2 · Q15(b) · 2 marks

She then packed the remaining fruits into as many bags as possible. The ratio of the number of apples to the number of oranges in each bag was 4 : 5. How many oranges were left unpacked?

Worked solution

252 - 70 = 182

Nan Hua 2025 · Paper 1 Booklet A · Q14 · 2 marks

The ratio of the number of girls in Team A to the number of girls in Team B is $2 : 3$. The ratio of the number of boys in Team A to the number of boys in Team B is $5 : 3$. In Team A, the ratio of the number of girls to the number of boys is $4 : 3$. What is the ratio of the number of girls to the number of boys in Team B?

1. $1 : 1$
2. $2 : 1$
3. $2 : 3$
4. $10 : 3$

Worked solution

\text{Let A girls} = 2k, B \text{ girls} = 3k
A \text{ boys} = 5m, B \text{ boys} = 3m
\text{In A: } 2k : 5m = 4 : 3
6k = 20m
k : m = 10 : 3
B \text{ girls} : B \text{ boys} = 3k : 3m = k : m = 10 : 3

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P6 Ratio Questions (with Worked Solutions)

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