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Harsh alone can complete 2/3rd of a coding project in 6 days. Sumit

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Bunuel
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Harsh alone can complete 2/3rd of a coding project in 6 days. Sumit [#permalink] New post   21 Jun 2021, 05:45
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Question Stats:

67% (03:35) correct 33% (03:28) wrong based on 124 sessions
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Harsh alone can complete 2/3rd of a coding project in 6 days. Sumit alone can complete 1/3rd of the same project in 8 days and Mini can complete 3/4th of the same work in 12 days. All of them started coding together. After 4 days, Harsh and Mini left the project. How many more days will be required by Sumit to complete the project?


(A) 2.33 days
(B) 2.67 days
(C) 3.33 days
(D) 3.67 days
(E) 4.33 days
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MarmikUpadhyay
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Re: Harsh alone can complete 2/3rd of a coding project in 6 days. Sumit [#permalink] New post   23 Jun 2021, 21:44
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Bunuel wrote:
Harsh alone can complete 2/3rd of a coding project in 6 days. Sumit alone can complete 1/3rd of the same project in 8 days and Mini can complete 3/4th of the
same work in 12 days. All of them started coding together. After 4 days, Harsh and Mini left the project. How many more days will be required by Sumit to complete the project?


(A) 2.33 days
(B) 2.67 days
(C) 3.33 days
(D) 3.67 days
(E) 4.33 days


Let, work done = w, rate of Harsh = h, rate of Sumit = s and rate of Mini = m.

From data:
\(h * 6 = \frac{2}{3} * w, s * 8 = \frac{1}{3} * w, m * 12 = \frac{3}{4} * w\)


=> \(h = \frac{w}{9}, s = \frac{w}{24}\) and \(m = \frac{w}{16}\).


Also given that,

\((h + s + m) * 4 + s * t = w \) [All 3 worked on project for 4 days, \(t\) is the time taken in days by Sumit to complete rest of the work]

=> \((\frac{w}{9} + \frac{w}{24} + \frac{w}{16}) * 4 + \frac{w}{24} * t = w\) [Rest is calculation]

=>\( t = 3.33 days\)

So, correct answer is option C.
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Re: Harsh alone can complete 2/3rd of a coding project in 6 days. Sumit [#permalink] New post   23 Jun 2021, 22:53
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Bunuel wrote:
Harsh alone can complete 2/3rd of a coding project in 6 days. Sumit alone can complete 1/3rd of the same project in 8 days and Mini can complete 3/4th of the
same work in 12 days. All of them started coding together. After 4 days, Harsh and Mini left the project. How many more days will be required by Sumit to complete the project?


(A) 2.33 days
(B) 2.67 days
(C) 3.33 days
(D) 3.67 days
(E) 4.33 days


Say there are 72 units in the project.
Harsh does 48 units in 6 days so he does 8 units/day.
Sumit does 24 units in 8 days so he does 3 units/day
Mini does 54 units in 12 days so she does 4.5 units/day.

Together in 4 days, they would do 4*(8 + 3 + 4.5) = 62 units.
10 units are left with Sumit will complete in 10/3 = 3.33 days

Answer (C)
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Re: Harsh alone can complete 2/3rd of a coding project in 6 days. Sumit [#permalink] New post   24 Jun 2021, 00:45
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Harsh alone can complete 2/3rd of a coding project in 6 days- therefore, he can complete 1/3rd in 3 days and hence he can complete the entire work in 9 days.
Sumit alone can complete 1/3rd of a coding project in 8 days- therefore, he can complete the entire work in 24 days.
Mini alone can complete 3/4th of a coding project in 12 days- therefore, he can complete 1/4th in 4 days and hence he can complete the entire work in 16 days.

Let the Coding project (the total work to be done) be worth 144 units. Note that 144 is the LCM of the number of days each person individually takes i.e. 144 = LCM (9, 24, 16).

If the total work = 144 units,

Rate of Harsh = 16 units per day
Rate of Sumit = 6 units per day
Rate of Mini = 9 units per day.

When all 3 work together, combined rate = 31 units per day.
Since they worked together for 4 days, the quantum of work accomplished = 31 * 4 = 124 units.

Remaining work in the Coding project = 144 – 124 = 20 units.

These 20 units will have to be completed by Sumit, working alone, since Harsh and Mini quit.
Time taken by Sumit = \(\frac{20 }{ 6}\) = 3.33 days. Sumit will take 3.33 days more to complete the remaining work after Harsha and Mini leave.

The correct answer option is C.
Hope that helps!
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Re: Harsh alone can complete 2/3rd of a coding project in 6 days. Sumit [#permalink] New post   28 Oct 2023, 03:15
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Re: Harsh alone can complete 2/3rd of a coding project in 6 days. Sumit [#permalink]
28 Oct 2023, 03:15
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