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A tank is fitted with two taps A and B. A can fill the tank totally in 45 minutes and B can purge the full tank in 60 minutes. On the off chance that both the taps are opened on the other hand for 1 minute, then in what amount of time the unfilled tank will be filled totally?
- a)2 hrs 55 min
- b)3 hrs 40 min
- c)5 hrs 53 min
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A tank is fitted with two taps A and B. A can fill the tank totally in...
Understanding the Problem
To determine how long it will take to fill the tank with taps A and B operating alternately, we first need to calculate the rates at which each tap works.
Tap A and Tap B Rates
- Tap A can fill the tank in 45 minutes, so its rate is 1/45 of the tank per minute.
- Tap B can empty the tank in 60 minutes, so its rate is -1/60 of the tank per minute (negative because it empties the tank).
Combined Rate of Operation
When both taps are opened alternately for 1 minute:
- In the first minute, Tap A fills: 1/45.
- In the second minute, Tap B empties: -1/60.
Net Effect of 2 Minutes
Calculating the net effect over a 2-minute cycle:
- Net fill in 2 minutes = (1/45 - 1/60).
To combine these fractions, we find a common denominator, which is 180:
- (4/180 - 3/180) = 1/180 of the tank filled every 2 minutes.
Time to Fill the Tank
To fill the entire tank:
- Since 1/180 of the tank is filled in 2 minutes, it will take 180 * 2 = 360 minutes to fill the tank completely.
Conversion of Time
360 minutes translates to:
- 6 hours.
Final Result
Since the options provided do not include 6 hours, the correct answer is:
- Option D: None of these.
To determine how long it will take to fill the tank with taps A and B operating alternately, we first need to calculate the rates at which each tap works.
Tap A and Tap B Rates
- Tap A can fill the tank in 45 minutes, so its rate is 1/45 of the tank per minute.
- Tap B can empty the tank in 60 minutes, so its rate is -1/60 of the tank per minute (negative because it empties the tank).
Combined Rate of Operation
When both taps are opened alternately for 1 minute:
- In the first minute, Tap A fills: 1/45.
- In the second minute, Tap B empties: -1/60.
Net Effect of 2 Minutes
Calculating the net effect over a 2-minute cycle:
- Net fill in 2 minutes = (1/45 - 1/60).
To combine these fractions, we find a common denominator, which is 180:
- (4/180 - 3/180) = 1/180 of the tank filled every 2 minutes.
Time to Fill the Tank
To fill the entire tank:
- Since 1/180 of the tank is filled in 2 minutes, it will take 180 * 2 = 360 minutes to fill the tank completely.
Conversion of Time
360 minutes translates to:
- 6 hours.
Final Result
Since the options provided do not include 6 hours, the correct answer is:
- Option D: None of these.
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Community Answer
A tank is fitted with two taps A and B. A can fill the tank totally in...
Work done by A in 1st minutes and B 2nd minute = (1/45- 1/60)= 1/180
Part filled in 2 min = 1/180
Part filled in 358 min = (1/360*358) = 358/360 = 179/180
Remaining part = (1-179/180) = 1/180
1/45 part is filled by A in (45*1/180) min= 1/4 min.
Total time taken to fill it = 358 1/4 min = 5 hrs.58 min 15 sec.
Part filled in 2 min = 1/180
Part filled in 358 min = (1/360*358) = 358/360 = 179/180
Remaining part = (1-179/180) = 1/180
1/45 part is filled by A in (45*1/180) min= 1/4 min.
Total time taken to fill it = 358 1/4 min = 5 hrs.58 min 15 sec.
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A tank is fitted with two taps A and B. A can fill the tank totally in 45 minutes and B can purge the full tank in 60 minutes. On the off chance that both the taps are opened on the other hand for 1 minute, then in what amount of time the unfilled tank will be filled totally?a)2 hrs 55 minb)3 hrs 40 minc)5 hrs 53 mind)none of theseCorrect answer is option 'D'. 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 A tank is fitted with two taps A and B. A can fill the tank totally in 45 minutes and B can purge the full tank in 60 minutes. On the off chance that both the taps are opened on the other hand for 1 minute, then in what amount of time the unfilled tank will be filled totally?a)2 hrs 55 minb)3 hrs 40 minc)5 hrs 53 mind)none of theseCorrect answer is option 'D'. 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 A tank is fitted with two taps A and B. A can fill the tank totally in 45 minutes and B can purge the full tank in 60 minutes. On the off chance that both the taps are opened on the other hand for 1 minute, then in what amount of time the unfilled tank will be filled totally?a)2 hrs 55 minb)3 hrs 40 minc)5 hrs 53 mind)none of theseCorrect answer is option 'D'. Can you explain this answer?.
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