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Hard Time and Work Question 1

If it takes 12 workers 20 days to complete a project, and if the project is started but after 10 days, 8 more workers join the team, how many more days will it take to complete the remaining work?

  1. 6 days
  2. 7 days
  3. 8 days
  4. 9 days

Correct Answer: B) 7 days

Explanation: First, let’s find out the total work done by 12 workers in 10 days. Total work = (Number of workers) × (Number of days) = 12 × 10 = 120 worker-days. After 10 days, 12 workers have completed 120 worker-days of work. So, remaining work = Total work – Work done in 10 days = 240 – 120 = 120 worker-days. Now, 8 more workers join the team, making the total workers 20. To find out how many more days it will take to complete the remaining work: Number of days = (Remaining work) / (Number of workers) = 120 / 20 = 6 days. So, it will take 6 more days to complete the remaining work, totaling 10 + 6 = 16 days. But since we started with 10 days, the additional days needed will be 16 – 10 = 6 days.


Hard Time and Work Question 2

If it takes 20 workers 12 days to complete a project, and if the efficiency of each worker decreases by 10%, how many more workers are needed to complete the same project in 10 days?

  1. 4 workers
  2. 5 workers
  3. 6 workers
  4. 7 workers

Correct Answer: C) 6 workers

Explanation: Initially, let’s find out the total work done by 20 workers in 12 days. Total work = (Number of workers) × (Number of days) = 20 × 12 = 240 worker-days. Now, if the efficiency of each worker decreases by 10%, it means each worker now does 90% of the original work in the same time. So, the new total work done by each worker = 90% of original work = 0.9 × 240 = 216 worker-days. To find out how many more workers are needed to complete the same project in 10 days: Number of workers = (Total work) / (Number of days) = 216 / 10 ≈ 21.6. Since we can’t have a fraction of a worker, we round up to the nearest whole number, which is 22. Initially, there were 20 workers, so additional workers needed = 22 – 20 = 2 workers. But if each worker is 90% efficient, then we need additional workers = (10% of original workers) = 0.1 × 20 = 2 workers. So, total additional workers needed = 2 + 2 = 4 workers.


Hard Time and Work Question 3

If it takes 18 workers 15 days to complete a project, and if the efficiency of each worker decreases by 20%, how many more days will it take for the same workers to complete the same project?

  1. 5 days
  2. 6 days
  3. 7 days
  4. 8 days

Correct Answer: B) 6 days

Explanation: Initially, let’s find out the total work done by 18 workers in 15 days. Total work = (Number of workers) × (Number of days) = 18 × 15 = 270 worker-days. Now, if the efficiency of each worker decreases by 20%, it means each worker now does 80% of the original work in the same time. So, the new total work done by each worker = 80% of original work = 0.8 × 270 = 216 worker-days. To find out how many more days it will take for the same workers to complete the same project: Number of days = (Total work) / (New total work done by each worker) = 270 / 216 ≈ 1.25 days. Since each worker is 80% efficient, it would take slightly more time, so the closest option is 1 day more, which is 6 days (Option B).


Hard Time and Work Question 4

If it takes 10 workers 18 days to complete a project, and if 4 workers leave after 6 days, how many more days will it take for the remaining workers to complete the same project?

  1. 8 days
  2. 9 days
  3. 10 days
  4. 12 days

Correct Answer: A) 8 days

Explanation: First, let’s find out the total work done by 10 workers in 6 days. Total work = (Number of workers) × (Number of days) = 10 × 6 = 60 worker-days. After 6 days, 10 workers have completed 60 worker-days of work. So, remaining work = Total work – Work done in 6 days = 180 – 60 = 120 worker-days. Now, if 4 workers leave, only 6 workers remain. To find out how many more days it will take for the remaining workers to complete the same project: Number of days = (Remaining work) / (Number of workers) = 120 / 6 = 20 days. But since they’ve already worked for 6 days, it will take 20 – 6 = 14 more days. So, total additional days needed = 14 days.


Hard Time and Work Question 5

If it takes 24 workers 10 days to complete a project, and if 8 workers join after 5 days, how many more days will it take for the remaining workers to complete the same project?

  1. 3 days
  2. 4 days
  3. 5 days
  4. 6 days

Correct Answer: C) 5 days

Explanation: First, let’s find out the total work done by 24 workers in 5 days. Total work = (Number of workers) × (Number of days) = 24 × 5 = 120 worker-days. After 5 days, 24 workers have completed 120 worker-days of work. So, remaining work = Total work – Work done in 5 days = 240 – 120 = 120 worker-days. Now, if 8 more workers join, the total workers become 32. To find out how many more days it will take for the remaining workers to complete the same project: Number of days = (Remaining work) / (Number of workers) = 120 / 32 ≈ 3.75 days. Since they’ve already worked for 5 days, it will take 3 more days. So, total additional days needed = 3 days.


Hard Time and Work Question 6

If it takes 30 workers 6 days to complete a project, and if the efficiency of each worker decreases by 25%, how many more days will it take for the same workers to complete the same project?

  1. 4 days
  2. 5 days
  3. 6 days
  4. 7 days

Correct Answer: B) 5 days

Explanation: Initially, let’s find out the total work done by 30 workers in 6 days. Total work = (Number of workers) × (Number of days) = 30 × 6 = 180 worker-days. Now, if the efficiency of each worker decreases by 25%, it means each worker now does 75% of the original work in the same time. So, the new total work done by each worker = 75% of original work = 0.75 × 180 = 135 worker-days. To find out how many more days it will take for the same workers to complete the same project: Number of days = (Total work) / (New total work done by each worker) = 180 / 135 ≈ 1.33 days. Since each worker is 75% efficient, it would take slightly more time, so the closest option is 1 day more, which is 5 days (Option B).


Hard Time and Work Question 7

If it takes 40 workers 8 days to complete a project, and if 20 workers leave after 4 days, how many more days will it take for the remaining workers to complete the same project?

  1. 4 days
  2. 6 days
  3. 8 days
  4. 10 days

Correct Answer: B) 6 days

Explanation: First, let’s find out the total work done by 40 workers in 4 days. Total work = (Number of workers) × (Number of days) = 40 × 4 = 160 worker-days. After 4 days, 40 workers have completed 160 worker-days of work. So, remaining work = Total work – Work done in 4 days = 320 – 160 = 160 worker-days. Now, if 20 workers leave, only 20 workers remain. To find out how many more days it will take for the remaining workers to complete the same project: Number of days = (Remaining work) / (Number of workers) = 160 / 20 = 8 days. But since they’ve already worked for 4 days, it will take 8 – 4 = 4 more days. So, total additional days needed = 4 days.


Hard Time and Work Question 8

If it takes 50 workers 5 days to complete a project, and if the efficiency of each worker decreases by 30%, how many more days will it take for the same workers to complete the same project?

  1. 5 days
  2. 6 days
  3. 7 days
  4. 8 days

Correct Answer: C) 7 days

Explanation: Initially, let’s find out the total work done by 50 workers in 5 days. Total work = (Number of workers) × (Number of days) = 50 × 5 = 250 worker-days. Now, if the efficiency of each worker decreases by 30%, it means each worker now does 70% of the original work in the same time. So, the new total work done by each worker = 70% of original work = 0.7 × 250 = 175 worker-days. To find out how many more days it will take for the same workers to complete the same project: Number of days = (Total work) / (New total work done by each worker) = 250 / 175 ≈ 1.43 days. Since each worker is 70% efficient, it would take slightly more time, so the closest option is 1 day more, which is 7 days (Option C).


Hard Time and Work Question 9

If it takes 60 workers 4 days to complete a project, and if the efficiency of each worker decreases by 40%, how many more days will it take for the same workers to complete the same project?

  1. 3 days
  2. 4 days
  3. 5 days
  4. 6 days

Correct Answer: A) 3 days

Explanation: Initially, let’s find out the total work done by 60 workers in 4 days. Total work = (Number of workers) × (Number of days) = 60 × 4 = 240 worker-days. Now, if the efficiency of each worker decreases by 40%, it means each worker now does 60% of the original work in the same time. So, the new total work done by each worker = 60% of original work = 0.6 × 240 = 144 worker-days. To find out how many more days it will take for the same workers to complete the same project: Number of days = (Total work) / (New total work done by each worker) = 240 / 144 ≈ 1.67 days. Since each worker is 60% efficient, it would take slightly less time, so the closest option is 1 day less, which is 3 days (Option A).