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A and B can do a piece of work in 10 days, while B and C can do the sa

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A and B can do a piece of work in 10 days, while B and C can do the sa  [#permalink]

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New post Updated on: 08 Nov 2016, 01:48
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A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?

A. 16
B. 32
C. 64
D. 96
E. None of These

Originally posted by Emdadul28 on 08 Nov 2016, 01:45.
Last edited by Bunuel on 08 Nov 2016, 01:48, edited 1 time in total.
Edited the question.
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Re: A and B can do a piece of work in 10 days, while B and C can do the sa  [#permalink]

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New post 08 Nov 2016, 02:03
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3
Emdadul28 wrote:
A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?

A. 16
B. 32
C. 64
D. 96
E. None of These


Let the rates of A, B and C be a, b, and c respectively.

A and B can do a piece of work in 10 days: a + b = 1/10;
B and C can do the same work in 15 days: b + c = 1/15;
C and A can do the same work in 25 days: c + a = 1/25.

Sum the above 3 equations: 2(a + b + c) = 31/150 --> a + b + c = 31/300
Subtract a + b = 1/10 from above to get c = 1/300.

For 4 days all 3 worked and completed 4*(a + b + a) = 124/300 of the work.
For the next 4 days B and C worked and they completed 4(b + c) = 4/15 = 80/300 of the work.

So, by the time C is left alone 1 - (124/300 + 80/300) = 96/300 of the work is left to be completed by C alone.
Time = Job/Rate = (96/300)/(1/300) = 96 days.

Answer: D.
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Re: A and B can do a piece of work in 10 days, while B and C can do the sa  [#permalink]

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New post 08 Nov 2016, 04:01
Bunuel wrote:
Emdadul28 wrote:
A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?

A. 16
B. 32
C. 64
D. 96
E. None of These


Let the rates of A, B and C be a, b, and c respectively.

A and B can do a piece of work in 10 days: a + b = 1/10;
B and C can do the same work in 15 days: b + c = 1/15;
C and A can do the same work in 25 days: c + a = 1/25.

Sum the above 3 equations: 2(a + b + c) = 31/150 --> a + b + c = 31/300
Subtract a + b = 1/10 from above to get c = 1/300.

For 4 days all 3 worked and completed 4*(a + b + a) = 124/300 of the work.
For the next 4 days B and C worked and they completed 4(b + c) = 4/15 = 80/300 of the work.

So, by the time C is left alone 1 - (124/300 + 80/300) = 96/300 of the work is left to be completed by C alone.
Time = Job/Rate = (96/300)/(1/300) = 96 days.

Answer: D.


Quote:
Assume that total units of work =LCM (10,15,25) = 60 units

Since A and B finish the work in 10 days, work done by them in a day = 60/10 = 6 units/day

AND B and C finish the work in 15 days, work done by them in a day = 60/15 = 4 units/day

AND C and A finish the work in 20 days, work done by them in a day = 60/20 = 3 units/day


@@@ Thanks for this. Can I do this math like this way? If so then help me to complete this math.
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Re: A and B can do a piece of work in 10 days, while B and C can do the sa  [#permalink]

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New post 08 Nov 2016, 05:35
Emdadul28 wrote:
Bunuel wrote:
Emdadul28 wrote:
A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?

A. 16
B. 32
C. 64
D. 96
E. None of These


Let the rates of A, B and C be a, b, and c respectively.

A and B can do a piece of work in 10 days: a + b = 1/10;
B and C can do the same work in 15 days: b + c = 1/15;
C and A can do the same work in 25 days: c + a = 1/25.

Sum the above 3 equations: 2(a + b + c) = 31/150 --> a + b + c = 31/300
Subtract a + b = 1/10 from above to get c = 1/300.

For 4 days all 3 worked and completed 4*(a + b + a) = 124/300 of the work.
For the next 4 days B and C worked and they completed 4(b + c) = 4/15 = 80/300 of the work.

So, by the time C is left alone 1 - (124/300 + 80/300) = 96/300 of the work is left to be completed by C alone.
Time = Job/Rate = (96/300)/(1/300) = 96 days.

Answer: D.


Quote:
Assume that total units of work =LCM (10,15,25) = 60 units

Since A and B finish the work in 10 days, work done by them in a day = 60/10 = 6 units/day

AND B and C finish the work in 15 days, work done by them in a day = 60/15 = 4 units/day

AND C and A finish the work in 20 days, work done by them in a day = 60/20 = 3 units/day


@@@ Thanks for this. Can I do this math like this way? If so then help me to complete this math.


You can continue basically exactly the same way with this approach.
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A and B can do a piece of work in 10 days, while B and C can do the sa  [#permalink]

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New post 08 Nov 2016, 06:06
Emdadul28 wrote:
Bunuel wrote:
Emdadul28 wrote:
A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?

A. 16
B. 32
C. 64
D. 96
E. None of These


Let the rates of A, B and C be a, b, and c respectively.

A and B can do a piece of work in 10 days: a + b = 1/10;
B and C can do the same work in 15 days: b + c = 1/15;
C and A can do the same work in 25 days: c + a = 1/25.

Sum the above 3 equations: 2(a + b + c) = 31/150 --> a + b + c = 31/300
Subtract a + b = 1/10 from above to get c = 1/300.

For 4 days all 3 worked and completed 4*(a + b + a) = 124/300 of the work.
For the next 4 days B and C worked and they completed 4(b + c) = 4/15 = 80/300 of the work.

So, by the time C is left alone 1 - (124/300 + 80/300) = 96/300 of the work is left to be completed by C alone.
Time = Job/Rate = (96/300)/(1/300) = 96 days.

Answer: D.


Quote:
Assume that total units of work =LCM (10,15,25) = 60 units LCM(10,15,25)=300

Since A and B finish the work in 10 days, work done by them in a day = 60/10 = 6 units/day 300/10= 30 units

AND B and C finish the work in 15 days, work done by them in a day = 60/15 = 4 units/day 300/15= 20 units

AND C and A finish the work in 20 days, work done by them in a day = 60/20 = 3 units/day
AND C and A finish the work in 25 days, work done by them in a day = 300/25 = 12 units/day


Certain data have been wrongly noted down

@@@ Thanks for this. Can I do this math like this way? If so then help me to complete this math.
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Re: A and B can do a piece of work in 10 days, while B and C can do the sa  [#permalink]

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New post 08 Nov 2016, 10:01
3
Emdadul28 wrote:
A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?

A. 16
B. 32
C. 64
D. 96
E. None of These


Let the total work be 150 units

Efficiency of A + B = 15 units/day
Efficiency of B + C = 10 units/day
Efficiency of A + C = 6 units/day

Efficiency of A + B + C = 15.5 units/day

So, Efficiency of A is = Efficiency of A + B + C - Efficiency of B + C

Or, Efficiency of A is = 15.5 - 10

Or, Efficiency of A is = 5.5

Similarly Efficiency of B is = 9.5 and, Efficiency of C is = 0.50


Quote:
they started working together, after 4 days A left.


Work done by A + B + C in 4 days is 15.5*4 = 62

Now, B + C works

Quote:
After another 4 days B left.


Work done by B + C in 4 days is 10*4 = 40 units

So, total work done is 102 units, and work left is 48 units..

Time taken by C to finish this work is \(\frac{48}{0.5}\) = 96 days...

Hence, answer will be (D) 96 days..

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Re: A and B can do a piece of work in 10 days, while B and C can do the sa  [#permalink]

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