Time and Work Question 1 - CAT 2022
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:
Step-by-Step Explanation
We apply the standard work-equivalence chain rule formula:
M₁ × D₁ × H₁/W₁ = M₂ × D₂ × H₂/W₂
- Initial State Parameters:
M₁ = N people, D₁ = 10 days, H₁ = 7 hours/day, W₁ = 0.35 (35% of the project)
- Subsequent State Parameters:
10 people left, so:
M₂ = N − 10 people
D₂ = 14 days
H₂ = 10 hours/day
Remaining work:
W₂ = 1 − 0.35 = 0.65 (65% of the project)
- Set Up and Solve the Equation:
(N × 10 × 7)/0.35 = ((N − 10) × 14 × 10)/0.65
70N/0.35 = 140(N − 10)/0.65
200N = 140(N − 10)/0.65
200N × 0.65 = 140(N − 10)
130N = 140N − 1400
10N = 1400
⟹ N = 140
Correct Option: D
💡 FundaMakers Tip:
Relying on the structural Chain Rule fraction bypasses the need to compute arbitrary intermediate absolute metrics like total man-hours. Setting up direct proportional balances helps you eliminate terms quickly across the equals sign.