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4 identical taps can fill a 100 liter tank in 6 hours, then

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4 identical taps can fill a 100 liter tank in 6 hours, then  [#permalink]

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New post 06 Sep 2018, 10:19
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4 identical taps can fill a 100 liter tank in 6 hours, then how many hours will be required to fill a 150 liter tank by 8 such taps?

A) 3
B)4
C)5
D)4.5
E)3.5

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Re: 4 identical taps can fill a 100 liter tank in 6 hours, then  [#permalink]

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New post 06 Sep 2018, 10:30
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divyajoshi12 wrote:
4 identical taps can fill a 100 liter tank in 6 hours, then how many hours will be required to fill a 150 liter tank by 8 such taps?

A) 3
B)4
C)5
D)4.5
E)3.5

Posted from my mobile device


OA: D

Water filled by 1 taps per hour \(= \frac{100}{6*4}\) Litre/hr

Water filled by 8 taps per hour \(= \frac{8*100}{6*4}\)Litre/hr

Time taken by 8 taps to fill 150 litre\(= \frac{150}{\frac{8*100}{6*4}}\)hr \(=\frac{150*6*4}{8*100}\)hr \(= 4.5\)hr
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Re: 4 identical taps can fill a 100 liter tank in 6 hours, then  [#permalink]

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New post 06 Sep 2018, 10:39
We can also do it in more simple way i.e. let's calculate the time it takes to fill 150 ltrs by 4 taps

=6/100*150 = 9 hours
Now since the taps are identical, we can simply half the time taken by 8 taps

=4.5 hrs

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4 identical taps can fill a 100 liter tank in 6 hours, then  [#permalink]

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New post 06 Sep 2018, 19:25
1
divyajoshi12 wrote:
4 identical taps can fill a 100 liter tank in 6 hours, then how many hours will be required to fill a 150 liter tank by 8 such taps?

A) 3
B)4
C)5
D)4.5
E)3.5

Alter the standard RT=W formula. Add "# of machines" (taps, workers, whatever) to LHS. Manipulate just as you would the standard formula.
(# of machines) * Rate * Time = Work

Scenario #1 Find individual tap rate: 4 identical taps can fill a 100L tank in 6 hrs

(# of machines) * R * T = W
\(4*R*6=100\)
\(R*24=100\)
\(R=\frac{100}{24}=\frac{25}{6}\)


At that rate for an individual tap, how many hours will it take for 8 such taps to fill a 150L tank?

Scenario #2: Find time needed in the new scenario. Use the rate just calculated.

(# of machines) * R * T = W
\(8*\frac{25}{6}*T=150\)
\(T*\frac{200}{6}=150\)
\(T*\frac{100}{3}=150\)

\(T=(150*\frac{3}{100})=(3*\frac{3}{2})=\frac{9}{2}=4.5\) hours

Answer D
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Re: 4 identical taps can fill a 100 liter tank in 6 hours, then  [#permalink]

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New post 06 Sep 2018, 19:44
6*(4/8)*(150/100)=4.5

First term is original time.
Second term 4/8 as time will decrease on increasing taps.
Third Term 150/100 as time will increase on increasing work.
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Re: 4 identical taps can fill a 100 liter tank in 6 hours, then &nbs [#permalink] 06 Sep 2018, 19:44
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