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 6 hours. Pipe A and pipe B together can fill it in 5 hours. How long would pipe B alone take to fill the tank?
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Answer: A
Let pipe A fill 1/6 of the tank each hour. Together, A and B fill 1/5 of the tank each hour. Rates add, so pipe B’s rate is the combined rate minus A’s rate. Pipe B’s rate = 1/5 – 1/6. Using common denominator 30, this is 6/30 – 5/30. That gives 1/30 tank per hour for pipe B. This reduces to 1/30 tank per hour. Time is the reciprocal of the rate: 30 hours. Check: 1/6 + 1/30 = 1/5, which equals 1/5.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q2. Pipe A can fill a tank in 11 hours. Pipe A and pipe B together can fill it in 10 hours. How long would pipe B alone take to fill the tank?
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Answer: C
Let pipe A fill 1/11 of the tank each hour. Together, A and B fill 1/10 of the tank each hour. Rates add, so pipe B’s rate is the combined rate minus A’s rate. Pipe B’s rate = 1/10 – 1/11. Using common denominator 110, this is 11/110 – 10/110. That gives 1/110 tank per hour for pipe B. This reduces to 1/110 tank per hour. Time is the reciprocal of the rate: 110 hours. Check: 1/11 + 1/110 = 1/10, which equals 1/10.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q3. Pipe A can fill a tank in 16 hours. Pipe A and pipe B together can fill it in 15 hours. How long would pipe B alone take to fill the tank?
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Answer: A
Let pipe A fill 1/16 of the tank each hour. Together, A and B fill 1/15 of the tank each hour. Rates add, so pipe B’s rate is the combined rate minus A’s rate. Pipe B’s rate = 1/15 – 1/16. Using common denominator 240, this is 16/240 – 15/240. That gives 1/240 tank per hour for pipe B. This reduces to 1/240 tank per hour. Time is the reciprocal of the rate: 240 hours. Check: 1/16 + 1/240 = 1/15, which equals 1/15.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q4. Pipe A can fill a tank in 8 hours. Pipe A and pipe B together can fill it in 4 hours. How long would pipe B alone take to fill the tank?
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Answer: D
Let pipe A fill 1/8 of the tank each hour. Together, A and B fill 1/4 of the tank each hour. Rates add, so pipe B’s rate is the combined rate minus A’s rate. Pipe B’s rate = 1/4 – 1/8. Using common denominator 32, this is 8/32 – 4/32. That gives 4/32 tank per hour for pipe B. This reduces to 1/8 tank per hour. Time is the reciprocal of the rate: 8 hours. Check: 1/8 + 1/8 = 1/4, which equals 1/4.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q5. Pipe A can fill a tank in 6 hours. Pipe A and pipe B together can fill it in 4 hours. How long would pipe B alone take to fill the tank?
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Answer: B
Let pipe A fill 1/6 of the tank each hour. Together, A and B fill 1/4 of the tank each hour. Rates add, so pipe B’s rate is the combined rate minus A’s rate. Pipe B’s rate = 1/4 – 1/6. Using common denominator 24, this is 6/24 – 4/24. That gives 2/24 tank per hour for pipe B. This reduces to 1/12 tank per hour. Time is the reciprocal of the rate: 12 hours. Check: 1/6 + 1/12 = 1/4, which equals 1/4.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q6. Pipe A can fill a tank in 25 hours. Pipe A and pipe B together can fill it in 24 hours. How long would pipe B alone take to fill the tank?
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Answer: A
Let pipe A fill 1/25 of the tank each hour. Together, A and B fill 1/24 of the tank each hour. Rates add, so pipe B’s rate is the combined rate minus A’s rate. Pipe B’s rate = 1/24 – 1/25. Using common denominator 600, this is 25/600 – 24/600. That gives 1/600 tank per hour for pipe B. This reduces to 1/600 tank per hour. Time is the reciprocal of the rate: 600 hours. Check: 1/25 + 1/600 = 1/24, which equals 1/24.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q7. Pipe A can fill a tank in 30 hours. Pipe A and pipe B together can fill it in 20 hours. How long would pipe B alone take to fill the tank?
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Answer: D
Let pipe A fill 1/30 of the tank each hour. Together, A and B fill 1/20 of the tank each hour. Rates add, so pipe B’s rate is the combined rate minus A’s rate. Pipe B’s rate = 1/20 – 1/30. Using common denominator 600, this is 30/600 – 20/600. That gives 10/600 tank per hour for pipe B. This reduces to 1/60 tank per hour. Time is the reciprocal of the rate: 60 hours. Check: 1/30 + 1/60 = 1/20, which equals 1/20.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q8. Pipe A can fill a tank in 22 hours. Pipe A and pipe B together can fill it in 21 hours. How long would pipe B alone take to fill the tank?
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Answer: C
Let pipe A fill 1/22 of the tank each hour. Together, A and B fill 1/21 of the tank each hour. Rates add, so pipe B’s rate is the combined rate minus A’s rate. Pipe B’s rate = 1/21 – 1/22. Using common denominator 462, this is 22/462 – 21/462. That gives 1/462 tank per hour for pipe B. This reduces to 1/462 tank per hour. Time is the reciprocal of the rate: 462 hours. Check: 1/22 + 1/462 = 1/21, which equals 1/21.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q9. Pipe A can fill a tank in 19 hours. Pipe A and pipe B together can fill it in 18 hours. How long would pipe B alone take to fill the tank?
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Answer: B
Let pipe A fill 1/19 of the tank each hour. Together, A and B fill 1/18 of the tank each hour. Rates add, so pipe B’s rate is the combined rate minus A’s rate. Pipe B’s rate = 1/18 – 1/19. Using common denominator 342, this is 19/342 – 18/342. That gives 1/342 tank per hour for pipe B. This reduces to 1/342 tank per hour. Time is the reciprocal of the rate: 342 hours. Check: 1/19 + 1/342 = 1/18, which equals 1/18.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q10. Pipe A can fill a tank in 10 hours. Pipe A and pipe B together can fill it in 6 hours. How long would pipe B alone take to fill the tank?
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Answer: C
Let pipe A fill 1/10 of the tank each hour. Together, A and B fill 1/6 of the tank each hour. Rates add, so pipe B’s rate is the combined rate minus A’s rate. Pipe B’s rate = 1/6 – 1/10. Using common denominator 60, this is 10/60 – 6/60. That gives 4/60 tank per hour for pipe B. This reduces to 1/15 tank per hour. Time is the reciprocal of the rate: 15 hours. Check: 1/10 + 1/15 = 1/6, which equals 1/6.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q11. Pipe A can fill a tank in 10 hours and pipe B in 4 hours. Both are opened together, but pipe B is closed after 2 hours. How long will pipe A take to fill the remaining part of the tank?
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Answer: B
Let pipe A fill 1/10 of the tank each hour. Let pipe B fill 1/4 of the tank each hour. Together their combined rate is 1/10 + 1/4 = 7/20 tank per hour. Both pipes run together for 2 hours. Work done together = 2 x 7/20 = 7/10 of the tank. Remaining work = 1 – 7/10 = 3/10 of the tank. Pipe A alone now works at 1/10 tank per hour. Time needed = 3/10 / (1/10) = 3/10 x 10 = 3 hours. Check: 2 hours together plus 3 hours of A alone completes exactly 1 tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q12. Pipe A can fill a tank in 20 hours and pipe B in 8 hours. Both are opened together, but pipe B is closed after 4 hours. How long will pipe A take to fill the remaining part of the tank?
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Answer: A
Let pipe A fill 1/20 of the tank each hour. Let pipe B fill 1/8 of the tank each hour. Together their combined rate is 1/20 + 1/8 = 7/40 tank per hour. Both pipes run together for 4 hours. Work done together = 4 x 7/40 = 7/10 of the tank. Remaining work = 1 – 7/10 = 3/10 of the tank. Pipe A alone now works at 1/20 tank per hour. Time needed = 3/10 / (1/20) = 3/10 x 20 = 6 hours. Check: 4 hours together plus 6 hours of A alone completes exactly 1 tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q13. Pipe A can fill a tank in 18 hours and pipe B in 8 hours. Both are opened together, but pipe B is closed after 4 hours. How long will pipe A take to fill the remaining part of the tank?
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Answer: D
Let pipe A fill 1/18 of the tank each hour. Let pipe B fill 1/8 of the tank each hour. Together their combined rate is 1/18 + 1/8 = 13/72 tank per hour. Both pipes run together for 4 hours. Work done together = 4 x 13/72 = 13/18 of the tank. Remaining work = 1 – 13/18 = 5/18 of the tank. Pipe A alone now works at 1/18 tank per hour. Time needed = 5/18 / (1/18) = 5/18 x 18 = 5 hours. Check: 4 hours together plus 5 hours of A alone completes exactly 1 tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q14. Pipe A can fill a tank in 10 hours and pipe B in 15 hours. Both are opened together, but pipe B is closed after 3 hours. How long will pipe A take to fill the remaining part of the tank?
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Answer: B
Let pipe A fill 1/10 of the tank each hour. Let pipe B fill 1/15 of the tank each hour. Together their combined rate is 1/10 + 1/15 = 1/6 tank per hour. Both pipes run together for 3 hours. Work done together = 3 x 1/6 = 1/2 of the tank. Remaining work = 1 – 1/2 = 1/2 of the tank. Pipe A alone now works at 1/10 tank per hour. Time needed = 1/2 / (1/10) = 1/2 x 10 = 5 hours. Check: 3 hours together plus 5 hours of A alone completes exactly 1 tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q15. Pipe A can fill a tank in 8 hours and pipe B in 6 hours. Both are opened together, but pipe B is closed after 3 hours. How long will pipe A take to fill the remaining part of the tank?
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Answer: A
Let pipe A fill 1/8 of the tank each hour. Let pipe B fill 1/6 of the tank each hour. Together their combined rate is 1/8 + 1/6 = 7/24 tank per hour. Both pipes run together for 3 hours. Work done together = 3 x 7/24 = 7/8 of the tank. Remaining work = 1 – 7/8 = 1/8 of the tank. Pipe A alone now works at 1/8 tank per hour. Time needed = 1/8 / (1/8) = 1/8 x 8 = 1 hour. Check: 3 hours together plus 1 hour of A alone completes exactly 1 tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q16. Pipe A can fill a tank in 10 hours and pipe B in 5 hours. Both are opened together, but pipe B is closed after 3 hours. How long will pipe A take to fill the remaining part of the tank?
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Answer: D
Let pipe A fill 1/10 of the tank each hour. Let pipe B fill 1/5 of the tank each hour. Together their combined rate is 1/10 + 1/5 = 3/10 tank per hour. Both pipes run together for 3 hours. Work done together = 3 x 3/10 = 9/10 of the tank. Remaining work = 1 – 9/10 = 1/10 of the tank. Pipe A alone now works at 1/10 tank per hour. Time needed = 1/10 / (1/10) = 1/10 x 10 = 1 hour. Check: 3 hours together plus 1 hour of A alone completes exactly 1 tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q17. Pipe A can fill a tank in 18 hours and pipe B in 9 hours. Both are opened together, but pipe B is closed after 3 hours. How long will pipe A take to fill the remaining part of the tank?
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Answer: C
Let pipe A fill 1/18 of the tank each hour. Let pipe B fill 1/9 of the tank each hour. Together their combined rate is 1/18 + 1/9 = 1/6 tank per hour. Both pipes run together for 3 hours. Work done together = 3 x 1/6 = 1/2 of the tank. Remaining work = 1 – 1/2 = 1/2 of the tank. Pipe A alone now works at 1/18 tank per hour. Time needed = 1/2 / (1/18) = 1/2 x 18 = 9 hours. Check: 3 hours together plus 9 hours of A alone completes exactly 1 tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q18. Pipe A can fill a tank in 12 hours and pipe B in 6 hours. Both are opened together, but pipe B is closed after 2 hours. How long will pipe A take to fill the remaining part of 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. Together their combined rate is 1/12 + 1/6 = 1/4 tank per hour. Both pipes run together for 2 hours. Work done together = 2 x 1/4 = 1/2 of the tank. Remaining work = 1 – 1/2 = 1/2 of the tank. Pipe A alone now works at 1/12 tank per hour. Time needed = 1/2 / (1/12) = 1/2 x 12 = 6 hours. Check: 2 hours together plus 6 hours of A alone completes exactly 1 tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q19. Pipe A can fill a tank in 16 hours and pipe B in 8 hours. Both are opened together, but pipe B is closed after 5 hours. How long will pipe A take to fill the remaining part of the tank?
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Answer: C
Let pipe A fill 1/16 of the tank each hour. Let pipe B fill 1/8 of the tank each hour. Together their combined rate is 1/16 + 1/8 = 3/16 tank per hour. Both pipes run together for 5 hours. Work done together = 5 x 3/16 = 15/16 of the tank. Remaining work = 1 – 15/16 = 1/16 of the tank. Pipe A alone now works at 1/16 tank per hour. Time needed = 1/16 / (1/16) = 1/16 x 16 = 1 hour. Check: 5 hours together plus 1 hour of A alone completes exactly 1 tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q20. Pipe A can fill a tank in 20 hours and pipe B in 4 hours. Both are opened together, but pipe B is closed after 3 hours. How long will pipe A take to fill the remaining part of the tank?
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Answer: A
Let pipe A fill 1/20 of the tank each hour. Let pipe B fill 1/4 of the tank each hour. Together their combined rate is 1/20 + 1/4 = 3/10 tank per hour. Both pipes run together for 3 hours. Work done together = 3 x 3/10 = 9/10 of the tank. Remaining work = 1 – 9/10 = 1/10 of the tank. Pipe A alone now works at 1/20 tank per hour. Time needed = 1/10 / (1/20) = 1/10 x 20 = 2 hours. Check: 3 hours together plus 2 hours of A alone completes exactly 1 tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q21. Pipe A can fill a tank in 12 hours and pipe B in 6 hours. Both are opened together, but pipe B is closed after 1 hour. How long will pipe A take to fill the remaining part of the tank?
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Answer: D
Let pipe A fill 1/12 of the tank each hour. Let pipe B fill 1/6 of the tank each hour. Together their combined rate is 1/12 + 1/6 = 1/4 tank per hour. Both pipes run together for 1 hour. Work done together = 1 x 1/4 = 1/4 of the tank. Remaining work = 1 – 1/4 = 3/4 of the tank. Pipe A alone now works at 1/12 tank per hour. Time needed = 3/4 / (1/12) = 3/4 x 12 = 9 hours. Check: 1 hour together plus 9 hours of A alone completes exactly 1 tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q22. Pipe A can fill a tank in 14 hours and pipe B in 8 hours. Both are opened together, but pipe B is closed after 4 hours. How long will pipe A take to fill the remaining part of the tank?
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Answer: C
Let pipe A fill 1/14 of the tank each hour. Let pipe B fill 1/8 of the tank each hour. Together their combined rate is 1/14 + 1/8 = 11/56 tank per hour. Both pipes run together for 4 hours. Work done together = 4 x 11/56 = 11/14 of the tank. Remaining work = 1 – 11/14 = 3/14 of the tank. Pipe A alone now works at 1/14 tank per hour. Time needed = 3/14 / (1/14) = 3/14 x 14 = 3 hours. Check: 4 hours together plus 3 hours of A alone completes exactly 1 tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q23. Pipe A can fill a tank in 10 hours and pipe B in 5 hours. Both are opened together, but pipe B is closed after 1 hour. How long will pipe A take to fill the remaining part of the tank?
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Answer: D
Let pipe A fill 1/10 of the tank each hour. Let pipe B fill 1/5 of the tank each hour. Together their combined rate is 1/10 + 1/5 = 3/10 tank per hour. Both pipes run together for 1 hour. Work done together = 1 x 3/10 = 3/10 of the tank. Remaining work = 1 – 3/10 = 7/10 of the tank. Pipe A alone now works at 1/10 tank per hour. Time needed = 7/10 / (1/10) = 7/10 x 10 = 7 hours. Check: 1 hour together plus 7 hours of A alone completes exactly 1 tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q24. Pipe A can fill a tank in 5 hours and pipe B in 10 hours. Both are opened together, but pipe B is closed after 2 hours. How long will pipe A take to fill the remaining part of the tank?
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Answer: B
Let pipe A fill 1/5 of the tank each hour. Let pipe B fill 1/10 of the tank each hour. Together their combined rate is 1/5 + 1/10 = 3/10 tank per hour. Both pipes run together for 2 hours. Work done together = 2 x 3/10 = 3/5 of the tank. Remaining work = 1 – 3/5 = 2/5 of the tank. Pipe A alone now works at 1/5 tank per hour. Time needed = 2/5 / (1/5) = 2/5 x 5 = 2 hours. Check: 2 hours together plus 2 hours of A alone completes exactly 1 tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
Q25. Pipe A can fill a tank in 6 hours and pipe B in 12 hours. Both are opened together, but pipe B is closed after 2 hours. How long will pipe A take to fill the remaining part of the tank?
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Answer: A
Let pipe A fill 1/6 of the tank each hour. Let pipe B fill 1/12 of the tank each hour. Together their combined rate is 1/6 + 1/12 = 1/4 tank per hour. Both pipes run together for 2 hours. Work done together = 2 x 1/4 = 1/2 of the tank. Remaining work = 1 – 1/2 = 1/2 of the tank. Pipe A alone now works at 1/6 tank per hour. Time needed = 1/2 / (1/6) = 1/2 x 6 = 3 hours. Check: 2 hours together plus 3 hours of A alone completes exactly 1 tank.
Related topics: Pipes and Cisterns: Formulas, Shortcuts and Solved Examples
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