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Three pipes A, B and C can fill a tank in 6 hours. After working at i

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Three pipes A, B and C can fill a tank in 6 hours. After working at i [#permalink]

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Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. How many hours will take C alone to fill the tank ?

A. 10
B. 12
C. 14
D. 16
E. 18
[Reveal] Spoiler: OA

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Re: Three pipes A, B and C can fill a tank in 6 hours. After working at i [#permalink]

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New post 10 Mar 2016, 20:00
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anceer wrote:
Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. How many hours will take C alone to fill the tank ?

A. 10
B. 12
C. 14
D. 16
E. 18


Hi,

INFO


1) ONE hour work of all three is 1/6
2) after two hours, C is closed

INFERENCE


1) In 2 hours all three would do 2/6 of work =1/3 of work..
2) remaining 2/3 rd of work is done by all three in 4 hours and by ONLY a and B in 7 hrs..


SOLUTION..


therefore lets find how much time C will take to complete this--
one hour work- 1/4-1/7=3/28..
so C takes 28/3 hour to complete 2/3 work..
so C will complete the entire work in 28/3 * 3/2=14 days..
C

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Re: Three pipes A, B and C can fill a tank in 6 hours. After working at i [#permalink]

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New post 03 Apr 2016, 00:20
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Combined rate of work
1/a+1/b+1/c=1/6
Work done by 3 in 2 hrs=2x1/6=1/3
Work left to be done
1-1/3=2/3.
This work is done by b&c in 7 hrs.
Thus Rate of work is
Work/time=2/3/7=2/21
Therefore
1/a-2/21=1/6. Solve the equation a=14 hrs

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Re: Three pipes A, B and C can fill a tank in 6 hours. After working at i [#permalink]

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New post 03 Apr 2016, 04:52
anceer wrote:
Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. How many hours will take C alone to fill the tank ?


Let the total capacity of the tank be 42 units (LCM of 2,6 & 7)

anceer wrote:
Three pipes A, B and C can fill a tank in 6 hours.


Efficiency of ABC is 42/7 = 6units/hr

anceer wrote:
After working at it together for 2 hours,


In 2 hours A B and C fill up 14 units of the tank , thus 28 units are left.

anceer wrote:
C is closed and A and B can fill the remaining part in 7 hours. How many hours will take C alone to fill the tank ?


A and B fill up 28 units in 7 hours thus efficiency of A & B is 4 units

We know , A+B+C = 7 and A + B = 4

So, Efficiency of C is 3 units/hr

Thus the time required to fill up the entire tank is 42/3 = 14 hours.
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Re: Three pipes A, B and C can fill a tank in 6 hours. After working at i [#permalink]

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New post 16 Sep 2016, 07:56
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i solved this way...
total work to be done = 6 parts.
all together can do 1 part in 1 hour.
2 hours passed - 2 parts were done. so left 4 parts to finish.
4 parts out of total 6 parts is 2/3.
now..A and B finish filling 2/3 in 7 hours. 2/3 divide by 7 = 2/21. this is the rate for A and B.
to find the rate for C, subtract from 1/6 (rate of all three pipes) the rate of A and B (2/21)
1/6 - 2/21 (multiply first fraction by 7, second by 2) = 7/42 - 4/42 = 3/42
now 3/42 is the rate of C. it can fill 3 pools in 42 hours, or one in 14 hours.
answer is C.

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Three pipes A, B and C can fill a tank in 6 hours. After working at i [#permalink]

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New post 15 Oct 2017, 17:03
anceer wrote:
Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. How many hours will take C alone to fill the tank ?

A. 10
B. 12
C. 14
D. 16
E. 18

1) Combined rate: A, B, and C fill one tank in six hours:

\(\frac{1}{A} +
\frac{1}{B} +
\frac{1}{C} = \frac{1}{6}\)

2) Amt of work finished, work remaining. They work at that rate for 2 hours. \(r*t = W\)

They finish:\((\frac{1}{6}* 2) = \frac{2}{6}= \frac{1}{3}\) tank

Remaining work: \((1 - \frac{1}{3})= \frac{2}{3}\) tank

3) Rate of A and B? C stops. A and B do remaining \(\frac{2}{3}\) in 7 hrs

A and B's combined rate? \(W/t = r\)

\(\frac{(\frac{2}{3})}{7}\) = \(\frac{2}{21}\)

That is, \(\frac{1}{A} +
\frac{1}{B} =
\frac{2}{21}\)

4) Find C's rate. Numbers aren't as bad as they look.

\(\frac{1}{A} +
\frac{1}{B} +
\frac{1}{C} = \frac{1}{6}\)

\(\frac{2}{21} +
\frac{1}{C} = \frac{1}{6}\)

Multiply each term by (6 * 21) = 126

\(12 + \frac{126}{C} = 21\)

\(\frac{126}{C} = 9\)

\(\frac{1}{C} = \frac{9}{126}=\) C's rate

5) C's time?
When work is 1, flip rate to get time. C's time: \(\frac{126}{9}\) = 14 hours

OR \((\frac{W}{r} = t)\):

\(\frac{1}{(\frac{9}{126})}\)

\(\frac{126}{9}
= 14\) hours

Answer C

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Three pipes A, B and C can fill a tank in 6 hours. After working at i   [#permalink] 15 Oct 2017, 17:03
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