Two pipes M and N can fill a tank in 30 and 45 minutes respectively. If both the pipes were open for few minutes after N was closed and the tank was full in 25 minutes, find the time for pipe N was open.a)8.16mb)7.5minc)5mind)10.2me)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

X(1/30+1/45) + 1/30(25-x) = 1
x/45+25/30 =1
x/45 = 5/30 =1/6
x=45/6
x=7.5m

Answer

A tap can fill a tank in 12 minutes and another tap can empty the tank in 6 minutes. If the tank is already full and then both the taps are opened the tank will be

Answer

Given:
Pipe M fills the tank in 30 minutes
Pipe N fills the tank in 45 minutes
Both pipes open for some time after N is closed and the tank is filled in 25 minutes

To find:
Time for pipe N was open

Approach:
Let's assume that pipe N was open for x minutes after it was closed

Using the formula:
Time = Work/Rate

Let's consider the work as filling the complete tank
So, work done by pipe M in 1 minute = 1/30
Work done by pipe N in 1 minute = 1/45

Since both pipes were open for some time and the tank was filled in 25 minutes, work done by both pipes together in 1 minute = 1/25

Let's calculate the work done by pipe N in x minutes after it was closed:
Work done by pipe N in x minutes = (1/45) * x

Now, let's calculate the work done by both pipes together in (25 - x) minutes:
Work done by both pipes together in (25 - x) minutes = (1/30 + 1/45) * (25 - x)

Since the tank is completely filled, the total work done by both pipes should be equal to the work required to fill the tank:
1 = (1/45) * x + (1/30 + 1/45) * (25 - x)

Solving the above equation, we get:
x = 7.5

Therefore, pipe N was open for 7.5 minutes.

Answer: Option B) 7.5 min

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