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If both the pipes are opened, how many hours will be taken to fill the tank?
I. The capacity of the tank is 400 litres.
II. The pipe A fills the tank in 4 hours.
III. The pipe B fills the tank in 6 hours.
I. The capacity of the tank is 400 litres.
II. The pipe A fills the tank in 4 hours.
III. The pipe B fills the tank in 6 hours.
- a)Only I and II
- b)Only II and III
- c)All I, II and III
- d)Any two of the three
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If both the pipes are opened, how many hours will be taken to fill the...
II. Part of the tank filled by A in 1 hour = 1/4
III. Part of the tank filled by B in 1 hour = 1/6
(A + B)’s 1 hour’s work = (1/4 + 1/6) = 5/12
∴ A and B will fill the tank in 12/5hrs
= 2 hrs 24 min.
So, II and III are needed.
∴ Correct answer is (b).
III. Part of the tank filled by B in 1 hour = 1/6
(A + B)’s 1 hour’s work = (1/4 + 1/6) = 5/12
∴ A and B will fill the tank in 12/5hrs
= 2 hrs 24 min.
So, II and III are needed.
∴ Correct answer is (b).
Most Upvoted Answer
If both the pipes are opened, how many hours will be taken to fill the...
To find out how many hours it will take to fill the tank when both pipes are opened, we need to consider the rates at which the pipes can fill the tank individually and when they are both open.
Statement I: The capacity of the tank is 400 litres.
This statement provides the capacity of the tank, which is useful information but does not directly help us determine the time taken to fill the tank.
Statement II: Pipe A fills the tank in 4 hours.
This statement tells us the time it takes for Pipe A to fill the tank. Since we know the capacity of the tank is 400 litres, we can calculate the rate at which Pipe A fills the tank. The rate of Pipe A is 400 liters / 4 hours = 100 liters per hour.
Statement III: Pipe B fills the tank in 6 hours.
Similarly, this statement tells us the time it takes for Pipe B to fill the tank. Using the same calculation, the rate of Pipe B is 400 liters / 6 hours = 66.67 liters per hour.
When both pipes are opened, we can add the rates at which they fill the tank to determine the combined rate. The combined rate is 100 liters per hour + 66.67 liters per hour = 166.67 liters per hour.
Therefore, when both pipes are opened, it will take 400 liters / 166.67 liters per hour = 2.4 hours to fill the tank.
Hence, the correct answer is option 'B' (Only II and III). Only statements II and III are required to determine the time taken to fill the tank when both pipes are opened.
Statement I: The capacity of the tank is 400 litres.
This statement provides the capacity of the tank, which is useful information but does not directly help us determine the time taken to fill the tank.
Statement II: Pipe A fills the tank in 4 hours.
This statement tells us the time it takes for Pipe A to fill the tank. Since we know the capacity of the tank is 400 litres, we can calculate the rate at which Pipe A fills the tank. The rate of Pipe A is 400 liters / 4 hours = 100 liters per hour.
Statement III: Pipe B fills the tank in 6 hours.
Similarly, this statement tells us the time it takes for Pipe B to fill the tank. Using the same calculation, the rate of Pipe B is 400 liters / 6 hours = 66.67 liters per hour.
When both pipes are opened, we can add the rates at which they fill the tank to determine the combined rate. The combined rate is 100 liters per hour + 66.67 liters per hour = 166.67 liters per hour.
Therefore, when both pipes are opened, it will take 400 liters / 166.67 liters per hour = 2.4 hours to fill the tank.
Hence, the correct answer is option 'B' (Only II and III). Only statements II and III are required to determine the time taken to fill the tank when both pipes are opened.
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