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A, B and C can do a work in 5 days, 10 days and 15 days respectively.

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A, B and C can do a work in 5 days, 10 days and 15 days respectively. [#permalink] New post   25 Jun 2019, 03:43
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A
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E

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35% (medium)

Question Stats:

73% (01:33) correct 27% (01:56) wrong based on 209 sessions
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A, B and C can do a work in 5 days, 10 days and 15 days respectively. They started together to do the work but after 2 days A and B left. C did the remaining work in how many days.

(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
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C
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Re: A, B and C can do a work in 5 days, 10 days and 15 days respectively. [#permalink] New post   25 Jun 2019, 03:51
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Bunuel wrote:
A, B and C can do a work in 5 days, 10 days and 15 days respectively. They started together to do the work but after 2 days A and B left. C did the remaining work in how many days.

(A) 6
(B) 5
(C) 4
(D) 3
(E) 2


Assume the total work = LCM(5, 10, 15) = 30 units

Rate of A = 30/5 = 6 units/day
Rate of B = 30/10 = 3 units/day
Rate of C = 30/15 = 2 units/day

If all of them work together, work done per day = 6 + 3 + 2 = 11 units
For 2 days, work done = 11*2 = 22

Work left after 2 days = 30 - 22 = 8 units

Time taken by C = work remaining/Raye of C
= 8/2 = 4 days

IMO Option C

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Re: A, B and C can do a work in 5 days, 10 days and 15 days respectively. [#permalink] New post   26 Jun 2019, 07:49
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Bunuel wrote:
A, B and C can do a work in 5 days, 10 days and 15 days respectively. They started together to do the work but after 2 days A and B left. C did the remaining work in how many days.

(A) 6
(B) 5
(C) 4
(D) 3
(E) 2


rate of A = 1/5
rate of B = 1/10
rate of C = 1/15
together total work done ; 1/5+1/10+1/15 = 11/30 *2 ; 11/15
left 4/15
so time it will take for C ; 4/15 * 15 = 4 days :)
IMO C
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Re: A, B and C can do a work in 5 days, 10 days and 15 days respectively. [#permalink] New post   28 Jun 2019, 01:26
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Solution



Given:
    • A, B and C can do a work in 5 days, 10 days and 15 days respectively
    • They started together to do the work.
      o After 2 days A and B left and C completed the remaining work.

To find:
    • C did the remaining work in how many days.

Approach and Working:
    • Let the total work = LCM(5, 10, 15) units = 30 Units
      o Hence, work done by A in 1 day = 6 units
         Work done by B in 1 day = 3 units
         Work done by B in 1 day = 2 units

Work done by A, B, and C in 2 days = 2* (6+3+2) = 22 units
    • Remaining work = 8 units
      o Time taken by C to complete 8 units of work =\(\frac{8}{2}\) = 4 days

Hence, the correct answer is option C.

Answer: C
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Re: A, B and C can do a work in 5 days, 10 days and 15 days respectively. [#permalink] New post   28 Jun 2019, 01:29
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Hey,

We have also posted an article on how to solve Time and work questions easily by using the LCM method.

To read the article: Solve Time and Work Problems Efficiently using Efficiency Method!

Regards,
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Re: A, B and C can do a work in 5 days, 10 days and 15 days respectively. [#permalink] New post   01 Jul 2019, 17:17
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Bunuel wrote:
A, B and C can do a work in 5 days, 10 days and 15 days respectively. They started together to do the work but after 2 days A and B left. C did the remaining work in how many days.

(A) 6
(B) 5
(C) 4
(D) 3
(E) 2



The combined rate of A, B, and C is:

1/5 + 1/10 + 1/15 = 6/30 + 3/30 + 2/30 = 11/30.

In two days 11/30 x 2 = 22/30 work is done, so 8/30 = 8/30 = 4/15 is left to be completed.

Thus, it takes C (4/15)/(1/15) = 60/15 = 4 days to complete the rest of the work.

Answer: C
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A, B and C can do a work in 5 days, 10 days and 15 days respectively. [#permalink] New post   11 Nov 2021, 10:56
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Assume that the total work = LCM(5, 10, 15) = 30 units
Work rate of A = 30/5= 6 units/day

Work rate of B = 30/10 = 3 units/day

Work rate of C = 30/15 = 2 units/day

If all of them work together, the work done per day= 6 + 3 + 2 = 11 units
For two days, the work done = 11*2= 22 units
Work left after 2 days = 30 - 22 = 8 units
Time taken by C = Work remaining/Rate of C = 8/2 = 4 days

Option C is the answer.

Thanks,
Clifin J Francis
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Re: A, B and C can do a work in 5 days, 10 days and 15 days respectively. [#permalink] New post   26 Nov 2023, 05:16
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Re: A, B and C can do a work in 5 days, 10 days and 15 days respectively. [#permalink]
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