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Pipes A, B and C can fill a tank in 3, 4 and 6 hours respectively. If all the pipes are opened together and after 30 minutes pipes B and C are turned off, find the total time in which the tank is full.
- a)2(3/8)hrs
- b)1(1/7)hrs
- c)2(2/7)hrs
- d)3(1/3)hrs
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Pipes A, B and C can fill a tank in 3, 4 and 6 hours respectively. If ...
In 1 hr A, B, C = 1/3+1/4+1/6 = 8+6+4/24 = 18/24 = 6/8 = ¾
Filled in 30m = 3/8
Remaining = 1-3/8 =5/8
Pipe A = 3*5/8 = 15/8
Total = 15/8+1/2 = 15+4/8 = 19/8 = 2(3/8) hrs
Filled in 30m = 3/8
Remaining = 1-3/8 =5/8
Pipe A = 3*5/8 = 15/8
Total = 15/8+1/2 = 15+4/8 = 19/8 = 2(3/8) hrs
Most Upvoted Answer
Pipes A, B and C can fill a tank in 3, 4 and 6 hours respectively. If ...
Solution:
Given:
- Pipe A fills the tank in 3 hours
- Pipe B fills the tank in 4 hours
- Pipe C fills the tank in 6 hours
- All pipes are opened together for 30 minutes
Approach:
- Find the rate at which each pipe fills the tank
- Calculate the amount of work done by all pipes in 30 minutes
- Find the remaining work to be done when pipes B and C are turned off
- Calculate the total time taken to fill the tank
Calculations:
- Rate of pipe A = 1/3 tank/hour
- Rate of pipe B = 1/4 tank/hour
- Rate of pipe C = 1/6 tank/hour
- All pipes open for 30 minutes = (1/3 + 1/4 + 1/6) * 0.5 = 11/12 of the tank filled
- Remaining work = 1 - 11/12 = 1/12 of the tank
- Pipes B and C turned off, only pipe A working
- Time taken by pipe A to fill 1/12 of the tank = (1/12) / (1/3) = 1/4 hour
- Total time taken = 30 minutes + 15 minutes = 45 minutes = 45/60 = 3/4 hours
Therefore, the total time taken to fill the tank is 3/4 hours which is equivalent to 2(3/8) hours. Hence, the correct answer is option A.
Given:
- Pipe A fills the tank in 3 hours
- Pipe B fills the tank in 4 hours
- Pipe C fills the tank in 6 hours
- All pipes are opened together for 30 minutes
Approach:
- Find the rate at which each pipe fills the tank
- Calculate the amount of work done by all pipes in 30 minutes
- Find the remaining work to be done when pipes B and C are turned off
- Calculate the total time taken to fill the tank
Calculations:
- Rate of pipe A = 1/3 tank/hour
- Rate of pipe B = 1/4 tank/hour
- Rate of pipe C = 1/6 tank/hour
- All pipes open for 30 minutes = (1/3 + 1/4 + 1/6) * 0.5 = 11/12 of the tank filled
- Remaining work = 1 - 11/12 = 1/12 of the tank
- Pipes B and C turned off, only pipe A working
- Time taken by pipe A to fill 1/12 of the tank = (1/12) / (1/3) = 1/4 hour
- Total time taken = 30 minutes + 15 minutes = 45 minutes = 45/60 = 3/4 hours
Therefore, the total time taken to fill the tank is 3/4 hours which is equivalent to 2(3/8) hours. Hence, the correct answer is option A.
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