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Two pipes A and B can fill a tank in 6 hours and 5 hours respectively. If they are turned on alternatively for 1 hour each, find the time in which the tank is full. (Assume pipe A is opened first)
- a)4hrs 30min
- b)5hrs
- c)6hrs 25min
- d)5hrs 30min
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Two pipes A and B can fill a tank in 6 hours and 5 hours respectively....
Total= 30, A = 30/6 =1/5, B = 30/5 =1/6
In 2 hrs = 5+6 =11
In 4hrs = 22
Remaining = 30-22 =8
1hr Pipe A = 8-5= 3,Remaining B = 3*1/6 = 30min
Total = 5hrs 30min
In 2 hrs = 5+6 =11
In 4hrs = 22
Remaining = 30-22 =8
1hr Pipe A = 8-5= 3,Remaining B = 3*1/6 = 30min
Total = 5hrs 30min
Most Upvoted Answer
Two pipes A and B can fill a tank in 6 hours and 5 hours respectively....
Given data:
- Pipe A fills the tank in 6 hours.
- Pipe B fills the tank in 5 hours.
- They are turned on alternatively for 1 hour each.
To find the time in which the tank is full, we need to calculate the combined filling rate of both pipes and determine how many times they need to be turned on alternately to fill the tank completely.
Let's calculate the filling rate of each pipe first:
- Pipe A fills the tank in 6 hours, so its filling rate is 1/6 of the tank per hour.
- Pipe B fills the tank in 5 hours, so its filling rate is 1/5 of the tank per hour.
Now, let's calculate the combined filling rate when both pipes are turned on:
- In the first hour, only Pipe A is turned on, so it fills 1/6 of the tank.
- In the second hour, only Pipe B is turned on, so it fills 1/5 of the tank.
- In the third hour, Pipe A is turned on again, filling another 1/6 of the tank.
- In the fourth hour, Pipe B is turned on again, filling another 1/5 of the tank.
This pattern continues alternately. We can see that in every 2 hours, the combined filling rate is 1/6 + 1/5 = 11/30 of the tank.
To find the time in which the tank is full, we need to determine how many times this combined filling rate fits into the tank. Let's denote the time taken for the tank to be full as T.
- In the first T hours, the combined filling rate fills T * (11/30) of the tank.
- Since the tank is full at the end of T hours, we have T * (11/30) = 1.
Solving this equation for T, we get T = 30/11 hours.
Converting this to hours and minutes, we have T = 2 hours and 42 minutes.
Since the pipes are turned on alternatively for 1 hour each, the total time taken to fill the tank will be slightly longer than T. It will be T + 1 hour.
So, the time taken to fill the tank is 2 hours and 42 minutes + 1 hour = 3 hours and 42 minutes.
However, none of the given answer options match the calculated time. Therefore, the correct answer is "None of these".
- Pipe A fills the tank in 6 hours.
- Pipe B fills the tank in 5 hours.
- They are turned on alternatively for 1 hour each.
To find the time in which the tank is full, we need to calculate the combined filling rate of both pipes and determine how many times they need to be turned on alternately to fill the tank completely.
Let's calculate the filling rate of each pipe first:
- Pipe A fills the tank in 6 hours, so its filling rate is 1/6 of the tank per hour.
- Pipe B fills the tank in 5 hours, so its filling rate is 1/5 of the tank per hour.
Now, let's calculate the combined filling rate when both pipes are turned on:
- In the first hour, only Pipe A is turned on, so it fills 1/6 of the tank.
- In the second hour, only Pipe B is turned on, so it fills 1/5 of the tank.
- In the third hour, Pipe A is turned on again, filling another 1/6 of the tank.
- In the fourth hour, Pipe B is turned on again, filling another 1/5 of the tank.
This pattern continues alternately. We can see that in every 2 hours, the combined filling rate is 1/6 + 1/5 = 11/30 of the tank.
To find the time in which the tank is full, we need to determine how many times this combined filling rate fits into the tank. Let's denote the time taken for the tank to be full as T.
- In the first T hours, the combined filling rate fills T * (11/30) of the tank.
- Since the tank is full at the end of T hours, we have T * (11/30) = 1.
Solving this equation for T, we get T = 30/11 hours.
Converting this to hours and minutes, we have T = 2 hours and 42 minutes.
Since the pipes are turned on alternatively for 1 hour each, the total time taken to fill the tank will be slightly longer than T. It will be T + 1 hour.
So, the time taken to fill the tank is 2 hours and 42 minutes + 1 hour = 3 hours and 42 minutes.
However, none of the given answer options match the calculated time. Therefore, the correct answer is "None of these".
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