This lesson gives each rule, the reason it works and seven worked examples. It also lists the traps that cost marks.
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Q1. Pipe A can fill a tank in 8 hours, and pipe B can fill it in 24 hours. If both pipes are opened together, how long will they take to fill the tank?
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Answer: C
Let pipe A fill 1/8 of the tank each hour. Let pipe B fill 1/24 of the tank each hour. Rates add when pipes work together. Combined rate = 1/8 + 1/24. Using common denominator 192, this is 24/192 + 8/192. That sums to 32/192 tank per hour. This reduces to 1/6 tank per hour. Time taken is the reciprocal of the rate: 6 hours. Check: 6 hours x 1/6 per hour = 1 whole tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q2. Pipe A can fill a tank in 6 hours, and pipe B can fill it in 30 hours. If both pipes are opened together, how long will they take to fill the tank?
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Answer: D
Let pipe A fill 1/6 of the tank each hour. Let pipe B fill 1/30 of the tank each hour. Rates add when pipes work together. Combined rate = 1/6 + 1/30. Using common denominator 180, this is 30/180 + 6/180. That sums to 36/180 tank per hour. This reduces to 1/5 tank per hour. Time taken is the reciprocal of the rate: 5 hours. Check: 5 hours x 1/5 per hour = 1 whole tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q3. Pipe A can fill a tank in 9 hours, and pipe B can fill it in 18 hours. If both pipes are opened together, how long will they take to fill the tank?
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Answer: A
Let pipe A fill 1/9 of the tank each hour. Let pipe B fill 1/18 of the tank each hour. Rates add when pipes work together. Combined rate = 1/9 + 1/18. Using common denominator 162, this is 18/162 + 9/162. That sums to 27/162 tank per hour. This reduces to 1/6 tank per hour. Time taken is the reciprocal of the rate: 6 hours. Check: 6 hours x 1/6 per hour = 1 whole tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q4. Pipe A can fill a tank in 12 hours, and pipe B can fill it in 6 hours. If both pipes are opened together, how long will they take to fill the tank?
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Answer: B
Let pipe A fill 1/12 of the tank each hour. Let pipe B fill 1/6 of the tank each hour. Rates add when pipes work together. Combined rate = 1/12 + 1/6. Using common denominator 72, this is 6/72 + 12/72. That sums to 18/72 tank per hour. This reduces to 1/4 tank per hour. Time taken is the reciprocal of the rate: 4 hours. Check: 4 hours x 1/4 per hour = 1 whole tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q5. Pipe A can fill a tank in 28 hours, and pipe B can fill it in 21 hours. If both pipes are opened together, how long will they take to fill the tank?
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Answer: C
Let pipe A fill 1/28 of the tank each hour. Let pipe B fill 1/21 of the tank each hour. Rates add when pipes work together. Combined rate = 1/28 + 1/21. Using common denominator 588, this is 21/588 + 28/588. That sums to 49/588 tank per hour. This reduces to 1/12 tank per hour. Time taken is the reciprocal of the rate: 12 hours. Check: 12 hours x 1/12 per hour = 1 whole tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q6. Pipe A can fill a tank in 6 hours, and pipe B can fill it in 12 hours. If both pipes are opened together, how long will they take to fill the tank?
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Answer: D
Let pipe A fill 1/6 of the tank each hour. Let pipe B fill 1/12 of the tank each hour. Rates add when pipes work together. Combined rate = 1/6 + 1/12. Using common denominator 72, this is 12/72 + 6/72. That sums to 18/72 tank per hour. This reduces to 1/4 tank per hour. Time taken is the reciprocal of the rate: 4 hours. Check: 4 hours x 1/4 per hour = 1 whole tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q7. Pipe A can fill a tank in 12 hours, and pipe B can fill it in 4 hours. If both pipes are opened together, how long will they take to fill the tank?
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Answer: A
Let pipe A fill 1/12 of the tank each hour. Let pipe B fill 1/4 of the tank each hour. Rates add when pipes work together. Combined rate = 1/12 + 1/4. Using common denominator 48, this is 4/48 + 12/48. That sums to 16/48 tank per hour. This reduces to 1/3 tank per hour. Time taken is the reciprocal of the rate: 3 hours. Check: 3 hours x 1/3 per hour = 1 whole tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q8. Pipe A can fill a tank in 20 hours, and pipe B can fill it in 30 hours. If both pipes are opened together, how long will they take to fill the tank?
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Answer: A
Let pipe A fill 1/20 of the tank each hour. Let pipe B fill 1/30 of the tank each hour. Rates add when pipes work together. Combined rate = 1/20 + 1/30. Using common denominator 600, this is 30/600 + 20/600. That sums to 50/600 tank per hour. This reduces to 1/12 tank per hour. Time taken is the reciprocal of the rate: 12 hours. Check: 12 hours x 1/12 per hour = 1 whole tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q9. Pipe A can fill a tank in 4 hours, and pipe B can fill it in 12 hours. If both pipes are opened together, how long will they take to fill the tank?
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Answer: D
Let pipe A fill 1/4 of the tank each hour. Let pipe B fill 1/12 of the tank each hour. Rates add when pipes work together. Combined rate = 1/4 + 1/12. Using common denominator 48, this is 12/48 + 4/48. That sums to 16/48 tank per hour. This reduces to 1/3 tank per hour. Time taken is the reciprocal of the rate: 3 hours. Check: 3 hours x 1/3 per hour = 1 whole tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q10. Pipe A can fill a tank in 5 hours, and pipe B can fill it in 20 hours. If both pipes are opened together, how long will they take to fill the tank?
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Answer: B
Let pipe A fill 1/5 of the tank each hour. Let pipe B fill 1/20 of the tank each hour. Rates add when pipes work together. Combined rate = 1/5 + 1/20. Using common denominator 100, this is 20/100 + 5/100. That sums to 25/100 tank per hour. This reduces to 1/4 tank per hour. Time taken is the reciprocal of the rate: 4 hours. Check: 4 hours x 1/4 per hour = 1 whole tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q11. Pipe A can fill a tank in 24 hours, and pipe B can fill it in 8 hours. If both pipes are opened together, how long will they take to fill the tank?
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Answer: C
Let pipe A fill 1/24 of the tank each hour. Let pipe B fill 1/8 of the tank each hour. Rates add when pipes work together. Combined rate = 1/24 + 1/8. Using common denominator 192, this is 8/192 + 24/192. That sums to 32/192 tank per hour. This reduces to 1/6 tank per hour. Time taken is the reciprocal of the rate: 6 hours. Check: 6 hours x 1/6 per hour = 1 whole tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples