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Secondary 4 Elementary Mathematics Numbers Ratio Proportion Quiz

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Questions

Secondary 4 Elementary Mathematics Quiz - Numbers Ratio Proportion

Name: ___________________________
Class: ___________________________
Date: ___________________________
Score: ________ / 40

Duration: 45 minutes
Total Marks: 40

Instructions:

Answer all questions.
Write your answers in the spaces provided.
Show all working clearly.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
The number of marks is given in brackets [ ] at the end of each question or part question.

Section A: Short Answer Questions (Questions 1–10, 2 marks each)

1. Express the ratio $4.5 : 1.2 : 3.6$ in its simplest form using whole numbers.
[2]

Answer: ___________________________

2. A sum of money is divided between Ali, Bala, and Cindy in the ratio $3 : 5 : 7$ . If Bala receives $120 more than Ali, find the total sum of money.
[2]

Answer: $___________________________

3. The scale of a map is $1 : 25\,000$ . The distance between two villages on the map is $8.4$ cm. Calculate the actual distance between the two villages in kilometres.
[2]

Answer: ___________________________ km

4. $y$ is inversely proportional to the square of $x$ . Given that $y = 12$ when $x = 2$ , find the value of $y$ when $x = 6$ .
[2]

Answer: ___________________________

5. A car travels $240$ km using $18$ litres of petrol. How many litres of petrol are needed to travel $400$ km at the same rate?
[2]

Answer: ___________________________ litres

6. The ratio of the number of boys to the number of girls in a class is $4 : 5$ . After $6$ boys join the class, the ratio becomes $1 : 1$ . How many students were in the class originally?
[2]

Answer: ___________________________

7. It takes $8$ workers $15$ days to complete a task. How many additional workers are needed to complete the same task in $10$ days, assuming all workers work at the same rate?
[2]

Answer: ___________________________

8. The price of a laptop is increased by $20\%$ and then decreased by $15\%$ . What is the overall percentage change in the price?
[2]

Answer: ___________________________%

9. A recipe for $12$ cupcakes requires $200$ g of flour, $150$ g of sugar, and $100$ g of butter. How much of each ingredient is needed to make $30$ cupcakes?
[2]

Answer: Flour = ____________ g, Sugar = ____________ g, Butter = ____________ g

10. $p$ is directly proportional to the cube root of $q$ . When $p = 6$ , $q = 27$ . Find the value of $p$ when $q = 64$ .
[2]

Answer: ___________________________

Section B: Structured Questions (Questions 11–16, 3 marks each)

11. A map has a scale of $1 : 50\,000$ .
(a) The area of a lake on the map is $12$ cm $^2$ . Calculate the actual area of the lake in km $^2$ .
[2]
(b) The actual length of a river is $25$ km. Calculate its length on the map in cm.
[1]

Answer (a): ___________________________ km $^2$
Answer (b): ___________________________ cm

12. The cost $C$ of producing $n$ items is given by $C = k\sqrt{n} + 50$ , where $k$ is a constant. When $25$ items are produced, the cost is $200$ .
(a) Find the value of $k$ .
[1]
(b) Find the cost of producing $100$ items.
[1]
(c) How many items can be produced for a cost of $350$ ?
[1]

Answer (a): $k =$ ___________________________
Answer (b): $___________________________
Answer (c): ___________________________ items

13. A rectangular tank measures $60$ cm by $40$ cm by $50$ cm. It is filled with water to a height of $30$ cm.
(a) Find the volume of water in the tank in litres.
[1]
(b) Water flows into the tank at a rate of $4$ litres per minute. How long will it take to fill the tank completely? Give your answer in minutes and seconds.
[2]

Answer (a): ___________________________ litres
Answer (b): ___________________________ minutes ___________________________ seconds

14. The ratio of the number of red marbles to blue marbles to green marbles in a bag is $3 : 4 : 5$ . There are $36$ more green marbles than red marbles.
(a) Find the total number of marbles in the bag.
[2]
(b) If $12$ blue marbles are removed, find the new ratio of red : blue : green marbles in its simplest form.
[1]

Answer (a): ___________________________
Answer (b): ___________________________

15. A car uses $1$ litre of petrol to travel $14$ km on the highway and $1$ litre to travel $10$ km in the city. A journey consists of $180$ km on the highway and $60$ km in the city.
(a) Calculate the total petrol consumption for the journey in litres.
[2]
(b) If petrol costs $2.80$ per litre, find the total cost of petrol for the journey.
[1]

Answer (a): ___________________________ litres
Answer (b): $___________________________

16. The time $T$ hours taken to paint a wall is inversely proportional to the number of painters $n$ . It takes $4$ painters $6$ hours to paint the wall.
(a) Write down an equation connecting $T$ and $n$ .
[1]
(b) Find the time taken if $8$ painters are used.
[1]
(c) How many painters are needed to paint the wall in $2$ hours?
[1]

Answer (a): ___________________________
Answer (b): ___________________________ hours
Answer (c): ___________________________ painters

Section C: Problem-Solving Questions (Questions 17–20, 4 marks each)

17. A factory produces two types of widgets, Type A and Type B, in the ratio $5 : 3$ . The production cost of Type A is $12$ per unit and Type B is $18$ per unit. The factory has a daily production budget of $12\,600$ .
(a) Find the maximum number of Type A widgets that can be produced in a day if the ratio must be maintained.
[2]
(b) Calculate the total number of widgets produced daily at this maximum.
[1]
(c) If the factory decides to produce $20\%$ more Type B widgets while keeping Type A production the same, find the new ratio of Type A : Type B in its simplest form.
[1]

Answer (a): ___________________________
Answer (b): ___________________________
Answer (c): ___________________________

18. A map is drawn to a scale of $1 : 40\,000$ . A rectangular plot of land measures $6$ cm by $4.5$ cm on the map.
(a) Find the actual dimensions of the plot in metres.
[2]
(b) Find the actual area of the plot in hectares. ( $1$ hectare $= 10\,000$ m $^2$ )
[2]

Answer (a): Length = ____________ m, Width = ____________ m
Answer (b): ___________________________ hectares

19. The pressure $P$ of a gas varies inversely as its volume $V$ . When the volume is $200$ cm $^3$ , the pressure is $150$ kPa.
(a) Find an equation connecting $P$ and $V$ .
[1]
(b) Calculate the pressure when the volume is reduced to $120$ cm $^3$ .
[1]
(c) The volume is increased by $50\%$ . Find the percentage change in the pressure.
[2]

Answer (a): ___________________________
Answer (b): ___________________________ kPa
Answer (c): ___________________________%

20. Three pipes, A, B, and C, can fill a tank. Pipe A alone takes $4$ hours, Pipe B alone takes $6$ hours, and Pipe C alone takes $12$ hours to fill the tank.
(a) What fraction of the tank is filled in $1$ hour when all three pipes are opened together?
[1]
(b) How long will it take to fill the tank completely with all three pipes opened?
[1]
(c) If Pipe A is opened for $1$ hour first, then all three pipes are opened together, how much additional time is needed to fill the tank?
[2]

Answer (a): ___________________________
Answer (b): ___________________________ hours
Answer (c): ___________________________ hours

End of Quiz

Answers

Secondary 4 Elementary Mathematics Quiz - Numbers Ratio Proportion (Answer Key)

Total Marks: 40

Section A: Short Answer Questions (Questions 1–10, 2 marks each)

1. Express the ratio $4.5 : 1.2 : 3.6$ in its simplest form using whole numbers.
[2]

Answer: $15 : 4 : 12$

Working:

Multiply all parts by 10 to remove decimals: $45 : 12 : 36$
Find HCF of 45, 12, 36: HCF = 3
Divide by 3: $15 : 4 : 12$

Marking: 1 mark for removing decimals correctly, 1 mark for correct simplified ratio.

2. A sum of money is divided between Ali, Bala, and Cindy in the ratio $3 : 5 : 7$ . If Bala receives $120 more than Ali, find the total sum of money.
[2]

Answer: $900$

Working:

Difference in ratio units between Bala and Ali = $5 - 3 = 2$ units
$2$ units = $120$
$1$ unit = $60$
Total units = $3 + 5 + 7 = 15$ units
Total sum = $15 \times 60 = 900$

Marking: 1 mark for finding value of 1 unit, 1 mark for correct total.

3. The scale of a map is $1 : 25\,000$ . The distance between two villages on the map is $8.4$ cm. Calculate the actual distance between the two villages in kilometres.
[2]

Answer: $2.1$ km

Working:

Actual distance = $8.4 \times 25\,000 = 210\,000$ cm
Convert to km: $210\,000 \div 100\,000 = 2.1$ km

Marking: 1 mark for correct multiplication, 1 mark for correct unit conversion and answer.

4. $y$ is inversely proportional to the square of $x$ . Given that $y = 12$ when $x = 2$ , find the value of $y$ when $x = 6$ .
[2]

Answer: $\frac{4}{3}$ or $1.33$ (3 s.f.)

Working:

$y = \frac{k}{x^2}$
$12 = \frac{k}{2^2} \Rightarrow k = 48$
When $x = 6$ , $y = \frac{48}{6^2} = \frac{48}{36} = \frac{4}{3}$

Marking: 1 mark for finding $k = 48$ , 1 mark for correct $y$ value.

5. A car travels $240$ km using $18$ litres of petrol. How many litres of petrol are needed to travel $400$ km at the same rate?
[2]

Answer: $30$ litres

Working:

Petrol consumption rate = $\frac{18}{240} = 0.075$ litres/km
Petrol for 400 km = $400 \times 0.075 = 30$ litres
Alternatively: $\frac{18}{240} = \frac{x}{400} \Rightarrow x = \frac{18 \times 400}{240} = 30$

Marking: 1 mark for correct method (unit rate or proportion), 1 mark for correct answer.

6. The ratio of the number of boys to the number of girls in a class is $4 : 5$ . After $6$ boys join the class, the ratio becomes $1 : 1$ . How many students were in the class originally?
[2]

Answer: $54$

Working:

Let original boys = $4u$ , girls = $5u$
After 6 boys join: $4u + 6 = 5u \Rightarrow u = 6$
Original total = $9u = 9 \times 6 = 54$

Marking: 1 mark for setting up equation correctly, 1 mark for correct answer.

7. It takes $8$ workers $15$ days to complete a task. How many additional workers are needed to complete the same task in $10$ days, assuming all workers work at the same rate?
[2]

Answer: $4$

Working:

Total work = $8 \times 15 = 120$ worker-days
Workers needed for 10 days = $120 \div 10 = 12$ workers
Additional workers = $12 - 8 = 4$

Marking: 1 mark for finding total work or using inverse proportion, 1 mark for correct additional workers.

8. The price of a laptop is increased by $20\%$ and then decreased by $15\%$ . What is the overall percentage change in the price?
[2]

Answer: $2\%$ increase

Working:

Let original price = $100$
After 20% increase: $100 \times 1.20 = 120$
After 15% decrease: $120 \times 0.85 = 102$
Overall change = $\frac{102 - 100}{100} \times 100\% = 2\%$ increase

Marking: 1 mark for correct sequential calculation, 1 mark for correct percentage change with direction.

9. A recipe for $12$ cupcakes requires $200$ g of flour, $150$ g of sugar, and $100$ g of butter. How much of each ingredient is needed to make $30$ cupcakes?
[2]

Answer: Flour = $500$ g, Sugar = $375$ g, Butter = $250$ g

Working:

Scale factor = $\frac{30}{12} = 2.5$
Flour: $200 \times 2.5 = 500$ g
Sugar: $150 \times 2.5 = 375$ g
Butter: $100 \times 2.5 = 250$ g

Marking: 1 mark for correct scale factor, 1 mark for all three correct amounts.

10. $p$ is directly proportional to the cube root of $q$ . When $p = 6$ , $q = 27$ . Find the value of $p$ when $q = 64$ .
[2]

Answer: $8$

Working:

$p = k\sqrt[3]{q}$
$6 = k\sqrt[3]{27} = 3k \Rightarrow k = 2$
When $q = 64$ , $p = 2 \times \sqrt[3]{64} = 2 \times 4 = 8$

Marking: 1 mark for finding $k = 2$ , 1 mark for correct $p$ value.

Section B: Structured Questions (Questions 11–16, 3 marks each)

11. A map has a scale of $1 : 50\,000$ .
(a) The area of a lake on the map is $12$ cm $^2$ . Calculate the actual area of the lake in km $^2$ .
[2]
(b) The actual length of a river is $25$ km. Calculate its length on the map in cm.
[1]

Answer (a): $3$ km $^2$
Answer (b): $50$ cm

Working (a):

Area scale factor = $(50\,000)^2 = 2.5 \times 10^9$
Actual area = $12 \times 2.5 \times 10^9 = 3 \times 10^{10}$ cm $^2$
Convert to km $^2$ : $3 \times 10^{10} \div (10^5)^2 = 3 \times 10^{10} \div 10^{10} = 3$ km $^2$

Working (b):

Map length = $\frac{25 \times 100\,000}{50\,000} = \frac{2\,500\,000}{50\,000} = 50$ cm

Marking (a): 1 mark for correct area scale factor, 1 mark for correct conversion to km $^2$ .
Marking (b): 1 mark for correct answer.

12. The cost $C$ of producing $n$ items is given by $C = k\sqrt{n} + 50$ , where $k$ is a constant. When $25$ items are produced, the cost is $200$ .
(a) Find the value of $k$ .
[1]
(b) Find the cost of producing $100$ items.
[1]
(c) How many items can be produced for a cost of $350$ ?
[1]

Answer (a): $k = 30$
Answer (b): $350$
Answer (c): $100$ items

Working (a):

$200 = k\sqrt{25} + 50 = 5k + 50$
$5k = 150 \Rightarrow k = 30$

Working (b):

$C = 30\sqrt{100} + 50 = 30 \times 10 + 50 = 350$

Working (c):

$350 = 30\sqrt{n} + 50$
$30\sqrt{n} = 300 \Rightarrow \sqrt{n} = 10 \Rightarrow n = 100$

Marking: 1 mark each for correct values.

13. A rectangular tank measures $60$ cm by $40$ cm by $50$ cm. It is filled with water to a height of $30$ cm.
(a) Find the volume of water in the tank in litres.
[1]
(b) Water flows into the tank at a rate of $4$ litres per minute. How long will it take to fill the tank completely? Give your answer in minutes and seconds.
[2]

Answer (a): $72$ litres
Answer (b): $12$ minutes $0$ seconds (or $12$ minutes)

Working (a):

Volume = $60 \times 40 \times 30 = 72\,000$ cm $^3 = 72$ litres

Working (b):

Tank capacity = $60 \times 40 \times 50 = 120\,000$ cm $^3 = 120$ litres
Remaining volume = $120 - 72 = 48$ litres
Time = $48 \div 4 = 12$ minutes = $12$ min $0$ sec

Marking (a): 1 mark for correct volume in litres.
Marking (b): 1 mark for correct remaining volume, 1 mark for correct time in minutes and seconds.

14. The ratio of the number of red marbles to blue marbles to green marbles in a bag is $3 : 4 : 5$ . There are $36$ more green marbles than red marbles.
(a) Find the total number of marbles in the bag.
[2]
(b) If $12$ blue marbles are removed, find the new ratio of red : blue : green marbles in its simplest form.
[1]

Answer (a): $144$
Answer (b): $3 : 2 : 5$

Working (a):

Difference in ratio units (green - red) = $5 - 3 = 2$ units
$2$ units = $36 \Rightarrow 1$ unit = $18$
Total units = $3 + 4 + 5 = 12$ units
Total marbles = $12 \times 18 = 144$

Working (b):

Red = $3 \times 18 = 54$ , Blue = $4 \times 18 = 72$ , Green = $5 \times 18 = 90$
After removing 12 blue: Blue = $72 - 12 = 60$
New ratio = $54 : 60 : 90 = 9 : 10 : 15$ (divide by 6) = $3 : 2 : 5$ (divide by 3? Wait: $54:60:90$ , divide by 6 = $9:10:15$ , divide by 3 = $3:2:5$ ? No, $9:10:15$ doesn't simplify to $3:2:5$ . Let me recalculate.)
$54 : 60 : 90$ , HCF = 6, so $9 : 10 : 15$ . That is the simplest form.
Wait, the answer I gave was $3:2:5$ . That's wrong. $54:60:90 = 9:10:15$ . Let me check: $54/18=3$ , $60/18=3.33$ , no. HCF of 54, 60, 90 is 6. So $9:10:15$ .
Correction: Answer (b) should be $9 : 10 : 15$ .

Corrected Answer (b): $9 : 10 : 15$

Marking (a): 1 mark for finding 1 unit = 18, 1 mark for correct total.
Marking (b): 1 mark for correct new ratio in simplest form.

15. A car uses $1$ litre of petrol to travel $14$ km on the highway and $1$ litre to travel $10$ km in the city. A journey consists of $180$ km on the highway and $60$ km in the city.
(a) Calculate the total petrol consumption for the journey in litres.
[2]
(b) If petrol costs $2.80$ per litre, find the total cost of petrol for the journey.
[1]

Answer (a): $\frac{174}{7}$ litres or $24\frac{6}{7}$ litres or $24.9$ litres (3 s.f.)
Answer (b): $69.60$

Working (a):

Highway petrol = $\frac{180}{14} = \frac{90}{7}$ litres
City petrol = $\frac{60}{10} = 6$ litres
Total = $\frac{90}{7} + 6 = \frac{90}{7} + \frac{42}{7} = \frac{132}{7} = 18\frac{6}{7}$ litres
Wait: $180/14 = 90/7 = 12.857$ , $60/10 = 6$ , total = $18.857 = 132/7 = 18\frac{6}{7}$ .
My previous answer $\frac{174}{7}$ was wrong. Let me recalculate: $180/14 = 90/7$ . $60/10 = 6 = 42/7$ . Sum = $132/7 = 18\frac{6}{7}$ .

Corrected Answer (a): $\frac{132}{7}$ litres or $18\frac{6}{7}$ litres or $18.9$ litres (3 s.f.)

Working (b):

Cost = $\frac{132}{7} \times 2.80 = \frac{132}{7} \times \frac{28}{10} = \frac{132 \times 4}{10} = \frac{528}{10} = 52.80$
Wait: $2.80 = 28/10 = 14/5$ . $\frac{132}{7} \times \frac{14}{5} = \frac{132 \times 2}{5} = \frac{264}{5} = 52.80$ .

Corrected Answer (b): $52.80$

Marking (a): 1 mark for correct highway petrol, 1 mark for correct total.
Marking (b): 1 mark for correct cost based on (a).

16. The time $T$ hours taken to paint a wall is inversely proportional to the number of painters $n$ . It takes $4$ painters $6$ hours to paint the wall.
(a) Write down an equation connecting $T$ and $n$ .
[1]
(b) Find the time taken if $8$ painters are used.
[1]
(c) How many painters are needed to paint the wall in $2$ hours?
[1]

Answer (a): $T = \frac{24}{n}$
Answer (b): $3$ hours
Answer (c): $12$ painters

Working (a):

$T = \frac{k}{n}$
$6 = \frac{k}{4} \Rightarrow k = 24$
Equation: $T = \frac{24}{n}$

Working (b):

$T = \frac{24}{8} = 3$ hours

Working (c):

$2 = \frac{24}{n} \Rightarrow n = 12$

Marking: 1 mark each for correct equation, time, and number of painters.

Section C: Problem-Solving Questions (Questions 17–20, 4 marks each)

17. A factory produces two types of widgets, Type A and Type B, in the ratio $5 : 3$ . The production cost of Type A is $12$ per unit and Type B is $18$ per unit. The factory has a daily production budget of $12\,600$ .
(a) Find the maximum number of Type A widgets that can be produced in a day if the ratio must be maintained.
[2]
(b) Calculate the total number of widgets produced daily at this maximum.
[1]
(c) If the factory decides to produce $20\%$ more Type B widgets while keeping Type A production the same, find the new ratio of Type A : Type B in its simplest form.
[1]

Answer (a): $525$
Answer (b): $840$
Answer (c): $25 : 18$

Working (a):

Let number of Type A = $5x$ , Type B = $3x$
Total cost = $12(5x) + 18(3x) = 60x + 54x = 114x$
$114x \leq 12\,600 \Rightarrow x \leq \frac{12\,600}{114} = 110.526...$
Maximum integer $x = 110$
Type A = $5 \times 110 = 550$
Wait, check: $114 \times 110 = 12\,540$ . $114 \times 111 = 12\,654 > 12\,600$ . So $x = 110$ .
Type A = $550$ .
My previous answer 525 was wrong. Let me recalculate carefully.
$12600 / 114 = 110.526$ . Integer part = 110. $5 \times 110 = 550$ .

Corrected Answer (a): $550$

Working (b):

Total widgets = $8x = 8 \times 110 = 880$

Corrected Answer (b): $880$

Working (c):

Type A = $550$ (unchanged)
Original Type B = $3 \times 110 = 330$
New Type B = $330 \times 1.2 = 396$
New ratio = $550 : 396$
Divide by 2: $275 : 198$
Divide by 11: $25 : 18$

Answer (c): $25 : 18$ (this part was correct based on the corrected numbers)

Marking (a): 1 mark for setting up cost equation, 1 mark for correct maximum integer value.
Marking (b): 1 mark for correct total based on (a).
Marking (c): 1 mark for correct new ratio in simplest form.

18. A map is drawn to a scale of $1 : 40\,000$ . A rectangular plot of land measures $6$ cm by $4.5$ cm on the map.
(a) Find the actual dimensions of the plot in metres.
[2]
(b) Find the actual area of the plot in hectares. ( $1$ hectare $= 10\,000$ m $^2$ )
[2]

Answer (a): Length = $2400$ m, Width = $1800$ m
Answer (b): $432$ hectares

Working (a):

Actual length = $6 \times 40\,000 = 240\,000$ cm = $2400$ m
Actual width = $4.5 \times 40\,000 = 180\,000$ cm = $1800$ m

Working (b):

Actual area = $2400 \times 1800 = 4\,320\,000$ m $^2$
Area in hectares = $4\,320\,000 \div 10\,000 = 432$ hectares

Marking (a): 1 mark for each correct dimension in metres.
Marking (b): 1 mark for correct area in m $^2$ , 1 mark for correct conversion to hectares.

19. The pressure $P$ of a gas varies inversely as its volume $V$ . When the volume is $200$ cm $^3$ , the pressure is $150$ kPa.
(a) Find an equation connecting $P$ and $V$ .
[1]
(b) Calculate the pressure when the volume is reduced to $120$ cm $^3$ .
[1]
(c) The volume is increased by $50\%$ . Find the percentage change in the pressure.
[2]

Answer (a): $P = \frac{30\,000}{V}$ or $PV = 30\,000$
Answer (b): $250$ kPa
Answer (c): $33.3\%$ decrease (or $-33.3\%$ )

Working (a):

$P = \frac{k}{V}$
$150 = \frac{k}{200} \Rightarrow k = 30\,000$
Equation: $P = \frac{30\,000}{V}$

Working (b):

$P = \frac{30\,000}{120} = 250$ kPa

Working (c):

New volume = $200 \times 1.5 = 300$ cm $^3$
New pressure = $\frac{30\,000}{300} = 100$ kPa
Percentage change = $\frac{100 - 150}{150} \times 100\% = -\frac{50}{150} \times 100\% = -33.3\%$
Pressure decreases by $33.3\%$

Marking (a): 1 mark for correct equation.
Marking (b): 1 mark for correct pressure.
Marking (c): 1 mark for correct new pressure, 1 mark for correct percentage change with direction.

20. Three pipes, A, B, and C, can fill a tank. Pipe A alone takes $4$ hours, Pipe B alone takes $6$ hours, and Pipe C alone takes $12$ hours to fill the tank.
(a) What fraction of the tank is filled in $1$ hour when all three pipes are opened together?
[1]
(b) How long will it take to fill the tank completely with all three pipes opened?
[1]
(c) If Pipe A is opened for $1$ hour first, then all three pipes are opened together, how much additional time is needed to fill the tank?
[2]

Answer (a): $\frac{1}{2}$
Answer (b): $2$ hours
Answer (c): $1$ hour

Working (a):

Rate of A = $\frac{1}{4}$ tank/hour
Rate of B = $\frac{1}{6}$ tank/hour
Rate of C = $\frac{1}{12}$ tank/hour
Combined rate = $\frac{1}{4} + \frac{1}{6} + \frac{1}{12} = \frac{3}{12} + \frac{2}{12} + \frac{1}{12} = \frac{6}{12} = \frac{1}{2}$ tank/hour
Fraction in 1 hour = $\frac{1}{2}$

Working (b):

Time = $1 \div \frac{1}{2} = 2$ hours

Working (c):

After 1 hour with Pipe A only: fraction filled = $\frac{1}{4}$
Remaining fraction = $1 - \frac{1}{4} = \frac{3}{4}$
Additional time = $\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times 2 = \frac{3}{2} = 1.5$ hours
Wait, my previous answer was 1 hour. Let me recalculate.
$\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times 2 = 1.5$ hours = 1 hour 30 minutes.
So answer should be $1.5$ hours or $1\frac{1}{2}$ hours.

Corrected Answer (c): $1.5$ hours (or $1\frac{1}{2}$ hours)

Marking (a): 1 mark for correct fraction.
Marking (b): 1 mark for correct time.
Marking (c): 1 mark for correct remaining fraction, 1 mark for correct additional time.

End of Answer Key