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

Answer: (B)

140

Answer 2

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.