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Pipe X and Z can filled a tank in 18 hours and in 4 hours. If pipe X is opened at 9:00 a.m and pipe Z is opened at 4:00 p.m, then at what time will the tank be filled.
- a)6:00 pm
- b)4:00 pm
- c)5:00 am
- d)9:00 pm
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Pipe X and Z can filled a tank in 18 hours and in 4 hours. If pipe X i...
Given
Pipe X filled a tank in 18 hours
Pipe Z filled a tank in 4 hours
Calculation
Total capacity of the tank = 36 units (i.e L.C.M of 18 and 4)
Tank filled by pipe X in 1 hour = 36/18
⇒ 2 units
Tank filled by pipe Z in 1 hour = 36/4
⇒ 9 units
Tank filled by pipe X in 7 hours = 2 × 7
⇒ 14 units
Remaining tank is filled by pipe X and Z = 36 - 14
⇒ 22 units
Tank filled in 1 hour by X and Z from 4:00 pm to 5:00 pm = 2 + 9
⇒ 11 units
Tank filled by X and Z from 5:00 pm to 6:00 pm = 2 + 9
⇒ 11 units
∴ Tank will be filled by 6:00 p.m
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Community Answer
Pipe X and Z can filled a tank in 18 hours and in 4 hours. If pipe X i...
Problem:
Pipe X and Z can fill a tank in 18 hours and 4 hours respectively. If pipe X is opened at 9:00 a.m and pipe Z is opened at 4:00 p.m, then at what time will the tank be filled?
Solution:
To solve this problem, we need to find the combined rate at which both pipes fill the tank and then calculate the time it takes to fill the tank using this rate.
Step 1: Calculate the individual rates of the pipes.
- Pipe X fills the tank in 18 hours, so its rate of filling is 1/18 of the tank per hour.
- Pipe Z fills the tank in 4 hours, so its rate of filling is 1/4 of the tank per hour.
Step 2: Calculate the combined rate of filling.
- To find the combined rate, we add the individual rates of the pipes.
- Combined rate = Rate of X + Rate of Z = 1/18 + 1/4 = (2 + 9)/36 = 11/36 of the tank per hour.
Step 3: Calculate the time taken to fill the tank.
- The tank is filled in 1 hour at a combined rate of 11/36 of the tank per hour.
- Therefore, the time taken to fill the tank completely is 36/11 hours.
Step 4: Calculate the time at which the tank will be filled.
- Pipe X is opened at 9:00 a.m and Pipe Z is opened at 4:00 p.m, which means Pipe X has been running for 7 hours before Pipe Z is opened.
- So, the total time taken to fill the tank will be 7 hours (time when Pipe Z is opened) + 36/11 hours (time taken to fill the tank completely).
- Simplifying, we get the total time as (77 + 36)/11 = 113/11 hours.
Final Answer:
The tank will be filled at 9:00 p.m, which is option 'A'.
Pipe X and Z can fill a tank in 18 hours and 4 hours respectively. If pipe X is opened at 9:00 a.m and pipe Z is opened at 4:00 p.m, then at what time will the tank be filled?
Solution:
To solve this problem, we need to find the combined rate at which both pipes fill the tank and then calculate the time it takes to fill the tank using this rate.
Step 1: Calculate the individual rates of the pipes.
- Pipe X fills the tank in 18 hours, so its rate of filling is 1/18 of the tank per hour.
- Pipe Z fills the tank in 4 hours, so its rate of filling is 1/4 of the tank per hour.
Step 2: Calculate the combined rate of filling.
- To find the combined rate, we add the individual rates of the pipes.
- Combined rate = Rate of X + Rate of Z = 1/18 + 1/4 = (2 + 9)/36 = 11/36 of the tank per hour.
Step 3: Calculate the time taken to fill the tank.
- The tank is filled in 1 hour at a combined rate of 11/36 of the tank per hour.
- Therefore, the time taken to fill the tank completely is 36/11 hours.
Step 4: Calculate the time at which the tank will be filled.
- Pipe X is opened at 9:00 a.m and Pipe Z is opened at 4:00 p.m, which means Pipe X has been running for 7 hours before Pipe Z is opened.
- So, the total time taken to fill the tank will be 7 hours (time when Pipe Z is opened) + 36/11 hours (time taken to fill the tank completely).
- Simplifying, we get the total time as (77 + 36)/11 = 113/11 hours.
Final Answer:
The tank will be filled at 9:00 p.m, which is option 'A'.
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