Quantitative Aptitude

Time, Work, and Projects

198 Questions

Time and work questions test the ability to calculate the time required to complete tasks involving individual or combined worker efficiency. These problems frequently appear in competitive exams to assess logical calculation skills. Topics include pipes, cisterns, group efficiency, and hourly work rates.

Combined work efficiencyMen and days calculationsWorker efficiency ratiosWorking hours per dayLeaving and joining workers

Time, Work, and Projects Questions

Multiple choice

A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 10th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5th day?

  1. 4

  2. 5

  3. 6

  4. 7
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

5 skilled workers can build a wall in 20 days, 8 semi-skilled workers can build a wall in 25 days, 10 unskilled workers can build a wall in 30 days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?

  1. 20

  2. 18

  3. 16

  4. 15
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Calculate the daily work rate for each worker type: skilled = 1/(5*20) = 1/100, semi-skilled = 1/(8*25) = 1/200, unskilled = 1/(10*30) = 1/300. The combined daily rate for the team is (2/100) + (6/200) + (5/300) = (6+9+5)/300 = 20/300 = 1/15. Thus, the time required is 15 days.

Multiple choice

For a particular project eight activities are to be carried out. Their relationships with other activities and excepted durations are mentioned in the table below:

Activity| Predecessors| Duration (days)| | a| -| 3| | b| a| 4| | c| a| 5| | d| a| 4| | e| b| 2| | f| d| 9| | g| c, e| 6| | h| f, g| 2|

If the duration of activity f alone is changed from 9 to 10 days, then the

  1. critical path remains the same and the total duration to complete the project changes to 19 days

  2. critical path and the total duration to complete the project remain the same

  3. critical path changes but the total duration to complete the project remains the same

  4. critical path changes and the total duration to complete the project changes to 17 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Multiple choice

A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 10th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5th day?

  1. 4

  2. 5

  3. 6

  4. 7
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Multiple choice business mathematics and statistics applications of calculus revenue functions from marginal revenue functions minimization of cost function and maximization of revenue function and profit function integral calculus – ii

A village road is to be constructed by a team of $250$ workers. After $12$ days it was found that only $2/7^{th}$ part of the work was complete. To complete the rest in another $25$ days, how many more workers should be employed?

  1. $53$
  2. $52$
  3. $55$
  4. $50$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the total unit of work be $7$ units.
According to question,
$\dfrac {M _{1}D _{1}}{W _{1}} = \dfrac {M _{2}D _{2}}{W _{2}} \Rightarrow \dfrac {250\times 12}{2} = \dfrac {M _{2}\times 25}{(7 - 2)} \Rightarrow M _{2} = 300$
Number of extra workers needed $= 300 - 250 = 50$.