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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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Manager
Joined: 04 Aug 2013
Posts: 96
Location: India
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GMAT 1: 670 Q47 V35
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WE: Manufacturing and Production (Pharmaceuticals and Biotech)
Three pipes A, B and C can fill a tank in 6 hours. After working at i  [#permalink]

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10 Mar 2016, 18:31
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12
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Difficulty:

35% (medium)

Question Stats:

73% (01:48) correct 27% (01:47) wrong based on 169 sessions

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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
Math Expert
Joined: 02 Aug 2009
Posts: 7025
Re: Three pipes A, B and C can fill a tank in 6 hours. After working at i  [#permalink]

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10 Mar 2016, 19:00
3
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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02 Apr 2016, 23:20
2
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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03 Apr 2016, 03:52
3
1
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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16 Sep 2016, 06:56
2
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.
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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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15 Oct 2017, 16:03
1
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

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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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11 Nov 2018, 22:57
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

A, B and C fill the tank in 6 hrs so their combined rate is 1/6 tank/hr
In 2 hrs, they will fill 1/3rd of the tank.

Now leftover 2/3rd of the tank is filled by A and B in 7 hrs. So combined rate of A and B = (2/3)/7 = 2/21 tank/hr

Rates are additive so,
Rate of C = Rate of A,B and C - Rate of A and B = 1/6 - 2/21 = 3/42 = 1/14
Hence, C alone will fill 1 tank in 14 hrs.

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Karishma
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Re: Three pipes A, B and C can fill a tank in 6 hours. After working at i &nbs [#permalink] 11 Nov 2018, 22:57
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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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