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# Carter can finish a task in 20 hours, Lucas can finish the same task

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Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3249
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21 Apr 2018, 10:55
3
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Difficulty:

45% (medium)

Question Stats:

72% (02:45) correct 28% (03:08) wrong based on 149 sessions

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Carter can finish a task in 20 hours, Lucas can finish the same task in 60 hours, and Lily can do so in 30 hours. Carter starts the work and is joined by Lucas after 10 hours. After another five hours, Carter leaves and Lily joins. How many more hours will the task take to finish?

A. 2 hours and 40 minutes
B. 3 hours
C. 3 hours and 20 minutes
D. 18 hours and 20 minutes
E. 18 hours and 40 minutes

Source: Experts Global

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21 Apr 2018, 12:37
1
Carter can finish a task in 20 hours, Lucas can finish the same task in 60 hours, and Lily can do so in 30 hours. Carter starts the work and is joined by Lucas after 10 hours. After another five hours, Carter leaves and Lily joins. How many hours will the task take to finish?

Leg 1: Carter starts the work and does the first leg of work for 10 hours. In 10 hours Carter would finish 50% of the task.

Leg 2: Lucas joins carter and they work together for 5 hours. In this 5 hours, carter would complete 25% of the total task and Lucas would complete 8.3% of the task.
In 5 hours Carter and Lucas joined together and would have completed 33.33% of the task.

Total: 83.33% of the task is completed.

Leg 3: Now Carter leaves and Lily joins Lucas.

Now lets test the answer choices. 16.66% of the task can be completed by Lucas alone in 10 hours. So if Lucas and Carter work together they will definitely complete in less than 10 hours. So we can eliminate choices D and E.

Next take choice B - 3 hours to test. In 3 hours Lily alone can complete 10% of the job and Lucas alone can complete 5% of the job. So together they can complete 15% of the job in 3 hours. We have 16.66% task to be completed. So our answer choice should be greater than 3 hours.

Only logical answer choice is Choice C - 3 Hours 20 Minutes

Ans: C
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21 Apr 2018, 13:15
manishbatra92 - Good Observation

In the question stem , the words "How many hours will the task take to finish?" is not clear. I calculated the remaining time to finish the task and chose Option C.

If the question is asking the total time taken to complete the task, then the answer would be 18 Hours and 20 Minutes - Option D
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21 Apr 2018, 19:08
1
2
pushpitkc wrote:
Carter can finish a task in 20 hours, Lucas can finish the same task in 60 hours, and Lily can do so in 30 hours. Carter starts the work and is joined by Lucas after 10 hours. After another five hours, Carter leaves and Lily joins. How many hours will the task take to finish?

A. 2 hours and 40 minutes
B. 3 hours
C. 3 hours and 20 minutes
D. 18 hours and 20 minutes
E. 18 hours and 40 minutes

Source: Experts Global

Carter's rate : $$\frac{1}{20}$$
Lucas's rate : $$\frac{1}{60}$$
Lily's rate: $$\frac{1}{30}$$

Stage 1: Carter works for 10 hours. (Carter starts and "is joined by Lucas after 10 hours")

WORK finished: $$r*t = W$$

W: $$(\frac{1}{20}*10)=\frac{10}{20}=\frac{1}{2}W$$
is finished

Work remaining: $$\frac{1}{2}W$$
Time used: 10 hours

Stage 2: Carter and Lucas work together for 5 hours
Combined work rate:
$$(\frac{1}{20}+\frac{1}{60})=(\frac{3}{60}+\frac{1}{60})=\frac{4}{60}=\frac{1}{15}$$

Work finished?
Together, C and L finish
W:$$(\frac{1}{15}*5)=\frac{1}{3}W$$

Work remaining: $$(\frac{1}{2}W-\frac{1}{3}W)=\frac{1}{6}W$$
Time used Stage 2: 5 hours

Stage 3: Lily and Lucas finish the job (Carter leaves)
Combined rate, L and L:
$$(\frac{1}{30}+\frac{1}{60})=(\frac{2}{60}+\frac{1}{60})=\frac{3}{60}=\frac{1}{20}$$

L and L have $$\frac{1}{6}W$$ to finish

TIME they require to finish?
$$T=\frac{W}{r}$$

$$T=\frac{\frac{1}{6}}{\frac{1}{20}}=(\frac{1}{6}*\frac{20}{1})=\frac{20}{6}=\frac{10}{3}=3\frac{1}{3}$$
hours

Total time taken to finish the work?

Stage 1 + Stage 2 + Stage 3 =
$$10 + 5 + 3\frac{1}{3}= 18\frac{1}{3}$$
hours

Total time = 18 hours, 20 minutes

"How many hours will the task take to finish?"

I agree, this statement is ambiguous. I think, however, that if the writers had meant "time for Lily and Lucas to finish," the writers would have asked, "How many hours will the rest of the task take to finish?"

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21 Apr 2018, 19:16
generis pushpitkc

In the question stem , the words "How many hours will the task take to finish?" looked little ambiguous.

I calculated the remaining time to finish the task and chose Option C.

If the question is asking the total time taken to complete the task, then the answer would be 18 Hours and 20 Minutes - Option D

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21 Apr 2018, 21:52
1
Apologies akadiyan , generis ,and manishbatra92

Made a small error in the question stem. Have made the correction now!

The corrected question stem now reads

Quote:
Carter can finish a task in 20 hours, Lucas can finish the same task in 60 hours, and Lily can do so in 30 hours. Carter starts the work and is joined by Lucas after 10 hours. After another five hours, Carter leaves and Lily joins. How many more hours will the task take to finish?

A. 2 hours and 40 minutes
B. 3 hours
C. 3 hours and 20 minutes
D. 18 hours and 20 minutes
E. 18 hours and 40 minutes

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22 Apr 2018, 03:13
Ans has to be C

Carlos completed 1/2 work in 10 hrs.
Lucas join him together they can complete work in 15 hrs but they have worked only for 5 hrs means they completed 1/3 work more.

Total work completed till now=1/2 +1/3=5/6

Lucas and Lucy complete work in 20 hrs.
But only 1/6 work is left. So time taken will be 20/6=3hrs 20 min

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22 Apr 2018, 04:08
I would agree with the majority, that it must be answer C.
Yes "How long will the task take to finish?" is ambiguous (Kudos for correcting quickly), but based on logic of the sentence (speaking from a language perspective) it describes a series of events with the question being asked as the last step in this series of events, thus implying that the remaining time must be asked for. Otherwise it would be a different tense/more specific sentence structure.
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Concentration: Accounting, Finance
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17 Dec 2018, 03:57
1
2
pushpitkc wrote:
Carter can finish a task in 20 hours, Lucas can finish the same task in 60 hours, and Lily can do so in 30 hours. Carter starts the work and is joined by Lucas after 10 hours. After another five hours, Carter leaves and Lily joins. How many more hours will the task take to finish?

A. 2 hours and 40 minutes
B. 3 hours
C. 3 hours and 20 minutes
D. 18 hours and 20 minutes
E. 18 hours and 40 minutes

Source: Experts Global

Carter's rate = 3 /hr
Lucas rate = 1 / hr
Lily's rate = 2/hr.

For 1st 10 hrs: 10*3 = 30 units.
For next 5 hrs( carter + lucas) = 4*5 = 20 units.

After carter leaves : ( Lily + Lucas)

Units left : 10.

So, Time : 10/3 = 3hr someting .

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16 May 2020, 06:17
Let the tesk be x
Carter finishes x/20 in one hr
Lucas finishes x/60 in one hr
And Lily finishes x/30 in one hr.
Carter would have completed half of the work in 10hours. Thus having x/2 of the work left before Lucas joined.
Lucas and carter working together will finish 1/20+1/60 of x=x/15
There for x/15 ×5 must have been completed by both thus x/3 must have been completed
Since x/2 is the work left after carter worked alone
x/2 – x/3 =x/6 will be left after both (Carter and Lucas) must have worked for 5 hours.
Lucas working will Lily
The work at 1/30+1/60=1/20 in one hour.
Hence p(x/20)=x/6
P= 20/6= 3hours 20 mins

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16 May 2020, 07:25
pushpitkc wrote:
Carter can finish a task in 20 hours, Lucas can finish the same task in 60 hours, and Lily can do so in 30 hours. Carter starts the work and is joined by Lucas after 10 hours. After another five hours, Carter leaves and Lily joins. How many more hours will the task take to finish?

A. 2 hours and 40 minutes
B. 3 hours
C. 3 hours and 20 minutes
D. 18 hours and 20 minutes
E. 18 hours and 40 minutes

Source: Experts Global

Let the total work be 60 units

So, Efficiency of Carter is 3 Units/hr , Efficiency of Lucas is 1 Units/hr & Efficiency of Lily is 2 Units/hr

Work done by Carter in 10 Hours is 30 units ; work left is 300 units
Quote:
After another five hours, Carter leaves and Lily joins.

So, Carter and Lucas works togather for 5 Hours

Hence, work done by Carter and Lucas in 5 Hours is 4*5 = 20 units ; work left is 10 units

Next , Only Lucas and Lily completes 10 units of work left in 10/3 hours = 3 hours 20 Minutes, Thus Answer must be (C)
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Re: Carter can finish a task in 20 hours, Lucas can finish the same task   [#permalink] 16 May 2020, 07:25