A pipe can empty a tank in 60 minutes alone. Another pipe whose diameter is twice the diameter of first pipe is also opened. Now find the time in which both pipe will empty the tank together.a)8 minb)10 minc)12 mind)14 mine)None of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Time taken by pipe to empty the tank is inversely proportional to cross- sectional area.
So, time taken by second pipe will be = 60/4 = 15 min (πr² = 1/60 and for second pipe 4πr² = 1/T so we get T = 15 min)
Time taken by both to empty the pipe = (60*15)/75 = 12

Answer

Let's assume that the capacity of the tank is 1 unit.

First, we need to find the rates at which each pipe can empty the tank.

The first pipe can empty the tank in 60 minutes, so its rate is 1/60 units per minute.

The second pipe has a diameter twice that of the first pipe. Since the rate of flow is directly proportional to the square of the diameter, the second pipe will have a rate four times that of the first pipe.

So, the rate of the second pipe is 4/60 = 1/15 units per minute.

Now, we need to find the combined rate at which both pipes can empty the tank.

To find the combined rate, we add the rates of both pipes:

Combined rate = 1/60 + 1/15
= (1 + 4)/60
= 5/60
= 1/12 units per minute

Now, let's calculate the time it will take for both pipes to empty the tank together.

Since the combined rate is 1/12 units per minute, it will take 12 minutes to empty 1 unit.

However, we assumed the capacity of the tank is 1 unit, so the time it will take to empty the tank is also 12 minutes.

Therefore, the correct answer is option 'C', 12 minutes.

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