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Pipe T1 can fill a cistern alone in 20 hours while another Pipe T2

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TheNightKing
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Pipe T1 can fill a cistern alone in 20 hours while another Pipe T2 [#permalink] New post   07 Feb 2020, 23:14
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45% (medium)

Question Stats:

68% (02:12) correct 32% (02:25) wrong based on 38 sessions
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Pipe T1 can fill a cistern alone in 20 hours while another Pipe T2 alone can empty the tank in 24 hours. If Pipe T2 is opened after 15 hours of starting of Pipe T1, then in how much time the tank will be filled?

(A) 40 hours
(B) 45 hours
(C) 44 hours
(D) 50 hours
(E) 20 hours­
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B
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Re: Pipe T1 can fill a cistern alone in 20 hours while another Pipe T2 [#permalink] New post   08 Feb 2020, 00:17
Rate of T1=1/20
Rate of T2=1/24

Rate when T1 and T2 are open=1/20-1/24=1/120

In 15 hours, T1 can fill

1/20*15=3/4

So 1/4 of the tank's capacity remains to be filled

After 15 hours,

1/120*t=1/4
t=30 hours

So the total time taken to fill the tank is 30+15=45hours

Answer is (B)

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Re: Pipe T1 can fill a cistern alone in 20 hours while another Pipe T2 [#permalink] New post   08 Feb 2020, 01:22
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Let us assume that the capacity of Tank is 120 Gallons

T1 can fill in the tank in 20 hours ==> The rate at which T1 fills in the tank is 6 Gallons per hour
T2 can empty the same tank in 24 hours ==> The rate at which T2 empties the tank is Gallons Gal per hour

Now: T1 fills in 90 Gallons in 15 hours ( 6 Gallons per hour)
The remaining capacity is 30 Gallons
Since T2 is now open, the Net Rate of Increase is : 6 - 5 = 1 Gallons per hour

With T1 and T2 both open the remaining 30 Gallons can be filled in 30 hours ( 1 Gallon per hour)

Therefore the total time : 15 + 30 = 45 Hours

Answer : (B)
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Re: Pipe T1 can fill a cistern alone in 20 hours while another Pipe T2 [#permalink]
08 Feb 2020, 01:22
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