Question

Q 37 Two pipes A and B can fill a tank in 30
minutes and 1.5 hours respectively.
Pipes A, B and a waste pipe Care
opened simultaneously. If pipe C is
closed after 36 minutes, it takes 24
minutes more to fill the tank. What is the
approximate time in which pipe C can
empty the tank along with pipe A?
Ops: A.
36 minutes
B.
77 minutes
C.
54 minutes
D
24 minutes​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

54 minutes (option C) will be the approximate time in which pipe C can empty the tank along with pipe A

Step-by-step explanation:

Let the rate of filling of pipe A be x and that of pipe B be y (in units of tank per minute). Then, we have:

x + y = 1/30 (since pipe A can fill the tank in 30 minutes)

x + 1.5y = 1/90 (since pipe B can fill the tank in 1.5 hours or 90 minutes)

Adding the two equations, we get:

2x + 2.5y = 1/30 + 1/90 = 2/45

=> 4x + 5y = 4/45 (multiplying both sides by 2)

Let the rate of the waste pipe C be z (in units of tank per minute). Then, we have:

x + y - z = 1/t (since all three pipes are opened simultaneously and fill the tank in time t)

After 36 minutes, the amount of water filled by pipes A and B is (x + y) × 36 = 36/t, and the amount of water emptied by pipe C is z × 36.

Therefore, the amount of water remaining to be filled after 36 minutes is 1 - 36/t + 36z.

We know that it takes 24 minutes more to fill the tank after pipe C is closed. This means that the remaining amount of water is filled by pipes A and B in 24 minutes at the rate of (x + y) tanks per minute.

So, we have:

24(x + y) = 1 - 36/t + 36z

=> 48x + 48y = 2t - 3 + 3t z (multiplying both sides by 2)

Substituting the value of 4x + 5y from the earlier equation, we get:

4/5 (2t - 3 + 3t z) = 4/45

Simplifying, we get:

8t - 12 + 12t z = 9

=> 8t + 12t z = 21

=> 4t + 6t z = 21/2

=> t + 3/2 t z = 21/8

We are asked to find the time taken by pipes A and C to empty the tank together. Let this time be u. Then, we have:

x - z = 1/u (since pipe C empties the tank)

Solving the two equations above simultaneously, we get:

z = (8 - 6t)/(12t) and u = 1/[(8 - 6t)/(12t) - x]

Substituting the values of x and t from the earlier equations, we get:

z = 1/36 and u = 54 minutes

Therefore, the approximate time in which pipe C can empty the tank along with pipe A is 54 minutes (option C).

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