Question

A group of N people worked on a project.They finished \(35\%\) of the project by working 7 hours a day for 10 days.Thereafter,10 people left the group and the remaining people finished the rest of the project in 14 days by working 10 hours a day.Then the value of N is

• A. 23
• B. 140
• C. 36
• D. 150

Answer 1

The Correct Option is B

The correct answer is B:140
In the first phase,the group finished \(35\%\) of the project by working 7 hours a day for 10 days. 
In the second phase,after 10 people left, the remaining people finished the rest of the project in 14 days by working 10 hours a day. 
Let's denote the total work required for the project as W. 
In the first phase: 
Work done=\(0.35 \times W\) 
Work rate=\((Number\space{of}\space people) \times (Hours\space per\space day) \times (Days) = N \times 7 \times 10\) 
In the second phase: 
Work done=\(0.65 \times W (since\space 100\% - 35\% = 65\%\space remains) \)
Work rate=\((Remaining\space number\space of\space people) \times 10 \times 14=(N - 10) \times 10 \times 14 \)
Since work done equals work rate in each phase, we can set up the following equations: 
\(0.35 \times W = N \times 7 \times 10 \)
\(0.65 \times W = (N - 10) \times 10 \times 14 \)
Now we can solve for N: 
From equation 1: \(W = \frac{(N \times 7 \times 10)}{0.35}\) 
From equation 2: \(W = \frac{((N - 10) \times 10 \times 14)}{0.65}\) 
Since both expressions are equal to W, we can set them equal to each other: 
\(\frac{(N \times 7 \times 10)}{0.35} = \frac{((N - 10) \times 10 \times 14)}{0.65 }\)
Now solve for N: 
\((N \times 7 \times 10 \times 0.65) = ((N - 10) \times 10 \times 14 \times 0.35) \)
Simplify: 
\(7 \times 10 \times 0.65 \times N = 10 \times 14 \times 0.35 \times (N - 10) \)
Now solve for N: 
\(4.55 \times N = 4.9 \times (N - 10) \)
Distribute on the right side: 
\(4.55 \times N = 4.9 \times (N - 49) \)
Subtract \(4.55 \times N\) from both sides: 
\(0.35 \times N = 49 \)
Now solve for N: 
\(N = \frac{49}{0.35} \)
N=140 
So,the initial number of people in the group (N) is 140. 

Answer 2

In 7 hours per day for 10 days, the work done by \(N\) people
\(=V \times 7 \times 10\) units
According to the question,
35% of the total work \(=N \times 7 \times 10\) units.
Total work done \(=\frac {(N \times 100 \times 7 \times 10)}{35}\) = \(200 \times N\) units.
The work left \(= 200 N - 70 N = 130 N\) units.
10 people left the job then the number of people left = \(N-10\)
Then,
\((N-10) \times 14\times 10=130N\)
\(10N = 1400\)
\(N = \frac {1400}{10}\)
\(N=140\)

So, the correct option is (B): \(140\)