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

A team completes 35% of a project in 10 days, working 7 hours daily. Subsequently, 10 members depart. The remaining team finishes the remaining 65% of the project in 14 days, working 10 hours daily. Determine the initial team size.

Step 1: Define Total Work as \( W \)

Initial Phase:

• Work Accomplished = \( 0.35W \)
• Let Original Team Size = \( N \)
• Total Man-Hours = \( N \times 7 \times 10 \)
• Equation: \( 0.35W = N \times 7 \times 10 \)

Subsequent Phase:

• Work Remaining = \( 0.65W \)
• Team Size After Departure = \( N - 10 \)
• Total Man-Hours = \( (N - 10) \times 10 \times 14 \)
• Equation: \( 0.65W = (N - 10) \times 10 \times 14 \)

Step 2: Equate Expressions for \( W \)

From the initial phase: \[ W = \frac{N \times 7 \times 10}{0.35} \] From the subsequent phase: \[ W = \frac{(N - 10) \times 10 \times 14}{0.65} \]

Equating the two expressions for \( W \): \[ \frac{N \times 7 \times 10}{0.35} = \frac{(N - 10) \times 10 \times 14}{0.65} \]

Step 3: Simplify the Equation

Cross-multiply: \[ N \times 7 \times 10 \times 0.65 = (N - 10) \times 10 \times 14 \times 0.35 \] \[ 70N \times 0.65 = 140(N - 10) \times 0.35 \] \[ 45.5N = 49(N - 10) \]

Step 4: Solve for \( N \)

Distribute: \[ 45.5N = 49N - 490 \] Rearrange terms: \[ 49N - 45.5N = 490 \] Combine like terms: \[ 3.5N = 490 \] Calculate \( N \): \( N = \frac{490}{3.5} = 140 \)

Conclusion:

\[ \boxed{140} \] The original number of people in the group was 140.

Corresponding Option: (B)