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Three taps A,B and C together can fill an empty cistern in 10 minutes. The tap A alone can fill it in 30 minutes and the tap B alone in 40 minutes. How long will the tap C alone take to fill it ?
- a)40 minutes
- b)16 minutes
- c)24 minutes
- d)32 minutes
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Three taps A,B and C together can fill an empty cistern in 10 minutes....
Using Rule 1 and 7,
Part of the cistern filled by taps
A, B and C in 1 minute = 1/10
Part of the cistern filled by taps
A and B in 1 minute
Part of the cistern filled by tap C in 1 minute
Tap C will fill the cistern in 24 minutes.
Part of the cistern filled by taps
A, B and C in 1 minute = 1/10
Part of the cistern filled by taps
A and B in 1 minute
Part of the cistern filled by tap C in 1 minute
Tap C will fill the cistern in 24 minutes.
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Community Answer
Three taps A,B and C together can fill an empty cistern in 10 minutes....
Understanding the Problem
We have three taps A, B, and C which can fill a cistern in different times. We need to find out how long tap C takes to fill the cistern alone.
Given Information
- All taps together (A, B, C) can fill the cistern in 10 minutes.
- Tap A alone can fill the cistern in 30 minutes.
- Tap B alone can fill the cistern in 40 minutes.
Filling Rates Calculation
- Rate of Tap A:
A fills 1/30 of the cistern per minute.
- Rate of Tap B:
B fills 1/40 of the cistern per minute.
- Rate of Tap C:
Let the rate of tap C be 1/x of the cistern per minute.
- Combined Rate:
Together, A, B, and C fill 1/10 of the cistern per minute.
Setting Up the Equation
We can set up the equation based on their combined rates:
(1/30) + (1/40) + (1/x) = 1/10
Finding a Common Denominator
- The least common multiple of 30, 40, and 10 is 120.
- Convert each rate to have a denominator of 120:
- (1/30) = 4/120
- (1/40) = 3/120
- (1/10) = 12/120
Now we can rewrite the equation:
4/120 + 3/120 + 1/x = 12/120
Solving for Tap C's Rate
- Combine the fractions:
(4 + 3)/120 + 1/x = 12/120
7/120 + 1/x = 12/120
- Rearranging gives us:
1/x = 12/120 - 7/120
1/x = 5/120
- Therefore, x = 24 minutes.
Conclusion
Thus, tap C alone will take 24 minutes to fill the cistern. The correct answer is option 'C'.
We have three taps A, B, and C which can fill a cistern in different times. We need to find out how long tap C takes to fill the cistern alone.
Given Information
- All taps together (A, B, C) can fill the cistern in 10 minutes.
- Tap A alone can fill the cistern in 30 minutes.
- Tap B alone can fill the cistern in 40 minutes.
Filling Rates Calculation
- Rate of Tap A:
A fills 1/30 of the cistern per minute.
- Rate of Tap B:
B fills 1/40 of the cistern per minute.
- Rate of Tap C:
Let the rate of tap C be 1/x of the cistern per minute.
- Combined Rate:
Together, A, B, and C fill 1/10 of the cistern per minute.
Setting Up the Equation
We can set up the equation based on their combined rates:
(1/30) + (1/40) + (1/x) = 1/10
Finding a Common Denominator
- The least common multiple of 30, 40, and 10 is 120.
- Convert each rate to have a denominator of 120:
- (1/30) = 4/120
- (1/40) = 3/120
- (1/10) = 12/120
Now we can rewrite the equation:
4/120 + 3/120 + 1/x = 12/120
Solving for Tap C's Rate
- Combine the fractions:
(4 + 3)/120 + 1/x = 12/120
7/120 + 1/x = 12/120
- Rearranging gives us:
1/x = 12/120 - 7/120
1/x = 5/120
- Therefore, x = 24 minutes.
Conclusion
Thus, tap C alone will take 24 minutes to fill the cistern. The correct answer is option 'C'.
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Question Description
Three taps A,B and C together can fill an empty cistern in 10 minutes. The tap A alone can fill it in 30 minutes and the tap B alone in 40 minutes. How long will the tap C alone take to fill it ?a)40 minutesb)16 minutesc)24 minutesd)32 minutesCorrect answer is option 'C'. Can you explain this answer? for SSC CGL 2026 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Three taps A,B and C together can fill an empty cistern in 10 minutes. The tap A alone can fill it in 30 minutes and the tap B alone in 40 minutes. How long will the tap C alone take to fill it ?a)40 minutesb)16 minutesc)24 minutesd)32 minutesCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three taps A,B and C together can fill an empty cistern in 10 minutes. The tap A alone can fill it in 30 minutes and the tap B alone in 40 minutes. How long will the tap C alone take to fill it ?a)40 minutesb)16 minutesc)24 minutesd)32 minutesCorrect answer is option 'C'. Can you explain this answer?.
Three taps A,B and C together can fill an empty cistern in 10 minutes. The tap A alone can fill it in 30 minutes and the tap B alone in 40 minutes. How long will the tap C alone take to fill it ?a)40 minutesb)16 minutesc)24 minutesd)32 minutesCorrect answer is option 'C'. Can you explain this answer? for SSC CGL 2026 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Three taps A,B and C together can fill an empty cistern in 10 minutes. The tap A alone can fill it in 30 minutes and the tap B alone in 40 minutes. How long will the tap C alone take to fill it ?a)40 minutesb)16 minutesc)24 minutesd)32 minutesCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three taps A,B and C together can fill an empty cistern in 10 minutes. The tap A alone can fill it in 30 minutes and the tap B alone in 40 minutes. How long will the tap C alone take to fill it ?a)40 minutesb)16 minutesc)24 minutesd)32 minutesCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Three taps A,B and C together can fill an empty cistern in 10 minutes. The tap A alone can fill it in 30 minutes and the tap B alone in 40 minutes. How long will the tap C alone take to fill it ?a)40 minutesb)16 minutesc)24 minutesd)32 minutesCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC CGL. Download more important topics, notes, lectures and mock test series for SSC CGL Exam by signing up for free.
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