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:
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 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:
Options
Answer: 140
Explanation:
Step 1: Define variables Let N = initial number of people Total work = 1 project unit Work done = People × Hours/day × Days Step 2: Work done by full group First phase: 35% of project = 0.35 units Number of people = N Hours/day = 7 Days = 10 Work done = N × 7 × 10 = 70 N person-hours Let total work in person-hours = W 0.35 × W = 70 N → W = 70 N / 0.35 = 200 N person-hours ✅ Total work W = 200 N person-hours Step 3: Work done by remaining group Remaining work = 1 - 0.35 = 0.65 units People remaining = N - 10 Hours/day = 10 Days = 14 Work done = (N - 10) × 10 × 14 = 140 × (N - 10) person-hours Remaining work in person-hours = 0.65 × W = 0.65 × 200 N = 130 N Equation: 140 × (N - 10) = 130 N Step 4: Solve for N 140 N - 1400 = 130 N 140 N - 130 N = 1400 10 N = 1400 N = 140 Answer: 140
Explanation:
Step 1: Define variables Let N = initial number of people Total work = 1 project unit Work done = People × Hours/day × Days Step 2: Work done by full group First phase: 35% of project = 0.35 units Number of people = N Hours/day = 7 Days = 10 Work done = N × 7 × 10 = 70 N person-hours Let total work in person-hours = W 0.35 × W = 70 N → W = 70 N / 0.35 = 200 N person-hours ✅ Total work W = 200 N person-hours Step 3: Work done by remaining group Remaining work = 1 - 0.35 = 0.65 units People remaining = N - 10 Hours/day = 10 Days = 14 Work done = (N - 10) × 10 × 14 = 140 × (N - 10) person-hours Remaining work in person-hours = 0.65 × W = 0.65 × 200 N = 130 N Equation: 140 × (N - 10) = 130 N Step 4: Solve for N 140 N - 1400 = 130 N 140 N - 130 N = 1400 10 N = 1400 N = 140 Answer: 140
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