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Given below are three quantities named A, B and C. Based on the given information; you have to determine the relationship between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. The options represent the relations between these three quantities A) > B) < C) = D) ≤ E) ≥ Two pipes P and Q can fill an empty tank in 20 minutes and 30 minutes respectively. Quantity A: If both pipes are opened simultaneously, then after what certain time P should be closed so that further time after which the tank is filled in 15 minutes? Quantity B: If both are opened and P is closed after 8 minutes, how much further time would it take for Q to fill the bucket? Quantity C: Pipe A and B can fill a tank in 15 minutes and 10 minutes respectively. Pipe C can empty the tank in 5 minutes. Pipe A and B are opened simultaneously and after the 4-minute pipe, C is also opened. In what time the tank will be emptied?

Given below are three quantities named A, B and C. Based on the given information; you have to determine the relationship between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. The options represent the relations between these three quantities A) > B) < C) = D) ≤ E) ≥ Two pipes P and Q can fill an empty tank in 20 minutes and 30 minutes respectively. Quantity A: If both pipes are opened simultaneously, then after what certain time P should be closed so that further time after which the tank is filled in 15 minutes? Quantity B: If both are opened and P is closed after 8 minutes, how much further time would it take for Q to fill the bucket? Quantity C: Pipe A and B can fill a tank in 15 minutes and 10 minutes respectively. Pipe C can empty the tank in 5 minutes. Pipe A and B are opened simultaneously and after the 4-minute pipe, C is also opened. In what time the tank will be emptied? Correct Answer B, B

Quantity A:

Let the total work = 60 units (LCM of 20 & 30)

⇒ Work done by P in 1 minute = 60/20 = 3 units

⇒ Work done by Q in 1 minute = 60/30 = 2 units

⇒ Work done by Q in 15 minutes = 30 units

⇒ Remaining work that was completed by P before being closed = 60 – 30 = 30 units

⇒ Time taken by P and Q to complete 30 units of work = 30/5 = 6 minutes

Quantity B:

Both the pipes were opened for 8 minutes then work completed = 8 × (3 + 2) = 40 units

⇒ Remaining work before P left = 60 – 40 = 20 units

⇒ Time taken by Q to complete 20 units of work = 20/2 = 10 minutes

Quantity C:

⇒ A’s work in 1 minute = 1/15

⇒ B’s work in 1 minute = 1/10

⇒ C’s work in 1 minute = - (1/5)            {it is emptying the tank}

⇒ (A + B)’s work in 1 minute = (1/15) + (1/10) =(1/6),

⇒ (A + B + C)’s work in 1 minute = (1/15) + (1/10) – (1/5) = - (1/30)

∵ Pipe A and B are opened for 4 minutes and then, tank filled in 4 minutes-

= 4×(1/6) = 2/3.

Now, pipe C is also opened, so time required to emptying the tank x

⇒ x/30 = 2/3

⇒ x = 20 min.

Hence, the required time to complete is 20 minutes.

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