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

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Intern
Joined: 06 Mar 2016
Posts: 15
4 identical taps can fill a 100 liter tank in 6 hours, then  [#permalink]

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06 Sep 2018, 09:19
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Difficulty:

15% (low)

Question Stats:

81% (01:00) correct 19% (00:50) wrong based on 59 sessions

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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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Joined: 18 Jun 2018
Posts: 231
Re: 4 identical taps can fill a 100 liter tank in 6 hours, then  [#permalink]

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06 Sep 2018, 09:30
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

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
Intern
Joined: 17 Aug 2018
Posts: 17
Re: 4 identical taps can fill a 100 liter tank in 6 hours, then  [#permalink]

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06 Sep 2018, 09:39
1
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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Senior SC Moderator
Joined: 22 May 2016
Posts: 2095
4 identical taps can fill a 100 liter tank in 6 hours, then  [#permalink]

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06 Sep 2018, 18:25
2
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

Change the standard RT=W formula.
Add "# of machines" (taps, workers, whatever) to LHS.
Manipulate it 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

Intern
Joined: 29 Aug 2018
Posts: 22
Re: 4 identical taps can fill a 100 liter tank in 6 hours, then  [#permalink]

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06 Sep 2018, 18:44
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.
Re: 4 identical taps can fill a 100 liter tank in 6 hours, then &nbs [#permalink] 06 Sep 2018, 18:44
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