vitorcbarbieri wrote:

Operating at a constant rate, 2 pumps of Type 1 can completely fill a reservoir with water in 24 hours. A pump of Type 2 can also fill the same reservoir with water but it operates at a different constant rate. At 1 PM on 21 March, 3 pumps of Type 2 start filling the empty reservoir. At 3 PM, 6 pumps of Type 1 also start filling the reservoir with water. The reservoir is completely filled with water at 7 PM. If the 6 Type 1 pumps were not started, at what time would the reservoir have been completely filled with water?

A) 1 AM on 22 March

B) 7 AM on 22 March

C) 1 AM on 23 March

D) 7 AM on 23 March

E) 7 AM on 25 March

Type 1 :

2 pumps can fill a reservoir in 24 hours.

So, 1 pump can fill reservoir in 48 hours.

In 1 hour 1 pump can fill 1/48th of reservoir.

Type 2 :

Let 1 pump of type 2 can fill a reservoir in x hours.

So, in 1 hour 1 pump of type 2 can fill 1/x th of reservoir.

At 1 PM on 21 March, 3 pumps of Type 2 start filling the empty reservoir. At 3 PM, 6 pumps of Type 1 also start filling the reservoir with water. The reservoir is completely filled with water at 7 PM.So, 3 pumps of type 2 is running for 6 hours and 6 pumps of type 1 is running for 4 hours.

Hence, 3*1/x*6 + 6*1/48*4 = 1

18/x +1/2 =1

x = 36.

So, 1 pump of type 2 can fill a reservoir in 36 hours.

If 6 pumps of Type 1 were not started. Only 3 pumps of type 2 had to fill the reservoir.

Time taken = 36/3 = 12 hours

So, reservoir would have been filled at 1 AM on 22nd march.

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