Compound Proportions

16 Grade 9 Mathematics questions on Compound Proportions, with worked marking schemes. 16 questions are available on this topic in full.

1. Question 1

   1 mark

   8 pumps can fill a tank in 15 hours. How long will 12 pumps take?

   A. 12 hours

   B. 8 hours

   C. 18 hours

   D. 10 hours

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

2. Question 2

   4 marks

   12 builders take 30 days to construct a house. After 10 days, 4 builders leave. How many more days will the remaining builders need to finish?

   (4 marks)

   Marking scheme for this question

   Create a free account to see it

3. Question 3

   1 mark

   If 3 litres of paint covers 15 m², how many litres cover 45 m²?

   A. 6 L

   B. 15 L

   C. 12 L

   D. 9 L

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

4. Question 4

   1 mark

   4 taps fill a bath in 12 minutes. How long will 6 taps take?

   A. 10 minutes

   B. 8 minutes

   C. 6 minutes

   D. 9 minutes

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

5. Question 5

   1 mark

   20 workers take 6 days to complete a job. If 5 workers are absent, how many days will it take?

   A. 9 days

   B. 8 days

   C. 10 days

   D. 7 days

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

6. Question 6

   1 mark

   A machine produces 480 items in 6 hours. How many items does it produce in 9 hours?

   A. 600

   B. 800

   C. 540

   D. 720

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

7. Question 7

   3 marks

   A quantity of food lasts 60 soldiers for 40 days. How long will it last 80 soldiers?

   (3 marks)

   Marking scheme for this question

   Create a free account to see it

8. Question 8

   3 marks

   A school needs 3,600 exercise books to last 6 months for 400 pupils. How many books are needed for the same period for 550 pupils?

   (3 marks)

   Marking scheme

   The books are shared among the pupils, so first find how many each pupil needs: $3,600÷400$. (1)

   $3,600÷400=9$ books for each pupil over the six months. (1)

   More pupils need proportionally more books, so multiply by $550$: $9\times 550=4,950$. (1)

   Final answer: $4,950$ books.

9. Question 9

   1 mark

   A car travels 240 km in 4 hours. How far does it travel in 7 hours at the same speed?

   A. 350 km

   B. 420 km

   C. 400 km

   D. 500 km

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

10. Question 10

    3 marks

    7 taps fill a tank in 20 minutes. How long will 4 taps take to fill the same tank?

    (3 marks)

    Marking scheme for this question

    Create a free account to see it

11. Question 11

    1 mark

    A motorist uses 12 litres of fuel for 180 km. How much fuel is needed for 300 km?

    A. 25 L

    B. 16 L

    C. 20 L

    D. 24 L

    (1 mark)

    Marking scheme for this question

    Create a free account to see it

12. Question 12

    1 mark

    5 men can dig a trench in 12 days. How many men are needed to dig it in 4 days?

    A. 20

    B. 10

    C. 15

    D. 8

    (1 mark)

    Marking scheme

    C. $15$ — this is inverse proportion: fewer days needs more men, so the total work $5\times 12=60$ man-days stays fixed. Then $60÷4=15$. B and D treat it as direct proportion, which would wrongly reduce the men.

13. Question 13

    3 marks

    At a tea factory in Kericho, $6$ workers pack $240$ kg of tea in $4$ hours. Working at the same rate, how many workers are needed to pack $600$ kg of tea in $5$ hours?

    (3 marks)

    Marking scheme

    More tea needs more workers (direct): factor $\frac{600}{240}$. Less time needs more workers (inverse): factor $\frac{4}{5}$. Workers $=6\times \frac{600}{240}\times \frac{4}{5}$ $=6\times 2.5\times 0.8$ $=12$. Check: rate $=\frac{240}{6\times 4}=10$ kg per worker-hour, so workers $=\frac{600}{10\times 5}=12$. Final answer: $12$ workers.

14. Question 14

    1 mark

    A recipe for 4 people uses 600 g of flour. How much flour is needed for 10 people?

    A. 1,200 g

    B. 1,500 g

    C. 1,000 g

    D. 2,000 g

    (1 mark)

    Marking scheme for this question

    Create a free account to see it

15. Question 15

    3 marks

    A factory produces 450 units in 5 days using 9 machines. How many days would 6 machines need to produce the same number of units?

    (3 marks)

    Marking scheme

    Fewer machines take longer, so machines and days are in inverse proportion: machines $\times$ days stays the same. (1)

    With $9$ machines and $5$ days, that total is $9\times 5=45$ machine-days. (1)

    With $6$ machines: $6\times d=45$, so $d=\frac{45}{6}=7.5$. (1)

    Final answer: $7.5$ days.

16. Question 16

    1 mark

    If 6 workers build a wall in 10 days, how long would 4 workers take (same rate)?

    A. 8 days

    B. 15 days

    C. 12 days

    D. 20 days

    (1 mark)

    Marking scheme for this question

    Create a free account to see it

17. 12 more marking schemes are on this page. A free account opens all of them, and lets you build your own paper on the topics you have actually taught, laid out in KNEC format with its full marking scheme.

    Create a free account

More Grade 9 Mathematics topics