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# Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r

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Re: Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r [#permalink]
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EgmatQuantExpert wrote:
3 Deadly Mistakes You Must Avoid in Time and Work Questions – Practice question 4

Leo, Shelly and Raj can complete a certain job in 10, 12, and 15 days respectively. They are assigned to work together to complete the job. All of them started the job together. Leo left 1 day before, and Raj left 2 days before the original scheduled completion day of the job. In how many days the job gets completed?

A. $$\frac{34}{5}$$ days

B. $$\frac{48}{5}$$ days

C. $$\frac{57}{12}$$ days

D. $$\frac{66}{15}$$ days

E. $$\frac{74}{15}$$ days

In 1 day together Leo, Shelly and Raj does = $$\frac{1}{10}+\frac{1}{12}+\frac{1}{15}$$ = $$\frac{(6+5+4)}{60}$$ = $$\frac{15}{60}$$ portion of the job.
==> they need 4 days if the were working on the job together.
According to the Q stem :
1.Leo, Shelly and Raj worked together for 2 days. hence the portion done= $$\frac{(15*2)}{60}=\frac{30}{60}$$
2. Then Leo & Shelly worked for 1 day . Hence the portion done =$$\frac{(6+5)}{60}$$ = $$\frac{11}{60}$$.... Thus the portion remaining= $$\frac{30}{60}-\frac{11}{60}=\frac{19}{60}$$... This is the portion Shelly worked alone
3. Hence time required for Shelly to complete $$\frac{19}{60}$$ portion of the work =work remaining/Shelly's daily working rate=$$\frac{19}{60}*\frac{60}{5}$$=$$\frac{19}{5}$$

Hence to tal days required : $$2+3+\frac{19}{60}= \frac{34}{5}$$..... Hence I would go for Option A.
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Re: Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r [#permalink]
let time shelly worked = t
leo = t-1
raj = t-2

[t][/12]+[t-1][/10]+[t-2][/15]=1
t=74/15

IMO ans should be E.

Bunuel
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Re: Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r [#permalink]
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failatmath wrote:
let time shelly worked = t
leo = t-1
raj = t-2

[t][/12]+[t-1][/10]+[t-2][/15]=1
t=74/15

IMO ans should be E.

Bunuel

Hey failatmath,
The question says "Leo left 1 day before, and Raj left 2 days before the original scheduled completion day of the job."

If you assume t as the total completion time, then for Leo and Raj, the working time is not t-1 and t-2. The 1-day less and 2-day less times are with respect to the originally scheduled completion time.

Check the solution above, and let us know if you have any confusion.
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Re: Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r [#permalink]
I understand the given solution. However, what am I doing wrong when I try the below. Please let me know.

Rate when all of them work together = 1/4

Rate when Leo and Shelly work together = 11/60

Rate when Shelly alone works = 1/12

Leo and Shelly worked for - 1 day

Shelly worked alone for - 1 day

Leo, Shelly and Raj worked together for x days

Now,

(x)1/4 + (1)11/60 + (1)1/12 = 1

therefore, x = 44/15

total days = 1 + 1 + 44/15 = 59/15

I know I am doing something wrong, just want to know what it is.

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Re: Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r [#permalink]
premprabhs111 wrote:

Leo and Shelly worked for - 1 day

Shelly worked alone for - 1 day

Hey premprabhs111,

check this line mentioned in the question: "Leo left 1 day before, and Raj left 2 days before the original scheduled completion day of the job."

As per you analysis, if the work finally completed in n days, then Raj worked for n-2 days and Leo worked for n-1 days.

However, as per the question statement, if the work would have been completed in d days(when all of them were working), then Raj worked for d-2 days and Leo worked for d-1 days. The values of n and d are not same.
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Re: Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r [#permalink]
L = 6/60 per day
S = 5/60 per day
R = 4/60 per day

Together = (6 + 5 + 4) / 60 = 15/60 per day = 4 days

15 units per day together, 60 units needed
R works 2 days
L works 3 days

15units x 2 = cumulative 30 units & 2 days
11units x 1 = cumulative 41 units & 3 days

19 units remain, 19 units over 5 units per day = 19/5 days + 3 earlier (15/5) = 34 / 5 days
Re: Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r [#permalink]
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