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. What is the value of $$ N $$?

Question

Accepted Answer

#### Step 1: Calculate Total Man-Hours for 35% of the Project  
- $$ N $$ people worked for 7 hours a day for 10 days to complete 35% of the project:

$$Total man-hours for 35\% = N × (7 × 10) = N × 70.$$

#### Step 2: Calculate Total Man-Hours for 65% of the Project  
- After completing 35%, the remaining 65% was completed by $$ N - 10 $$ people working for 14 days at 10 hours per day:

$$Total man-hours for 65\% = (N − 10) × (14 × 10) = (N − 10) × 140.$$

#### Step 3: Equate Total Man-Hours  
Since both groups worked on the same project, their total man-hours must be proportional to the percentage of work completed:  
$$
N 	imes 70 = (N - 10) 	imes 140.
$$

#### Step 4: Solve for $$ N $$  
Simplify the equation:  
$$
70N = 140N - 1400.
$$  
Rearrange terms:  
$$
1400 = 140N - 70N.
$$  
$$
1400 = 70N.
$$  
Solve for $$ N $$:  
$$
N = \frac{1400}{70} = 140.
$$

### Final Answer:  
The value of $$ N $$ is **140**, and the correct answer is **B**.

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