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X can do a piece of work alone in 20 days, if he devotes 9 hours daily. However X works alone on the 1st day and on the 2nd day one man whose capacity to do the work is twice as that of X, joined in. On the 3rd day, another man whose capacity is thrice as that of X, joined and similarly on the 4th day, another man whose capacity is four times as that of X, joined them. The process continues this way until the work is completed. On which day will the work be completed, if everyone works for five hours a day?
  • a)
    5th day
  • b)
    6th day
  • c)
    7th day
  • d)
    8th day
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
X can do a piece of work alone in 20 days, if he devotes 9 hours daily...
Since X takes 20 days working 9 hours a day to complete the work, the total man - hours required to complete this work would be 180 man - hours.
Amount of work done in the 1st day by X = 5 hours = 5 man - hours
On the 2nd day, X does again 5 man - hours of work. The 2nd person being twice as efficient as X, will do double the work that X does, which is 10 man - hours of work.
Total work done on 2nd day = 5 + 10 = 15 man - hours
3rd day, X does 5 man - hours of work. 2nd person does 10 man - hours of work. 3rd person who is thrice as efficient as X does 15 man - hours of work.
Total work done on 3rd day = 5 + 10 + 15 = 30 man - hours
Similarly on 4th day the amount of work done would be = 5 + 10 + 15 + 20 = 50 man - hours
Similarly on 5th day the amount of work done would be = 5 + 10 + 15 + 20 + 25 = 75 man - hours
Total work done after 5 days = 5 + 15 + 30 + 50 + 75 = 175 man - hours.
On the 6th day the work remaining will be 5 man - hours.
but on the 6th day the amount of work that can be done is = 5 + 10 + 15 +20 + 25 + 30 = 105 man - hours.
Thus we can see that the work will be complete on the 6th day itself.
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Most Upvoted Answer
X can do a piece of work alone in 20 days, if he devotes 9 hours daily...
Understanding the Work Capacity
- X can complete the work in 20 days by working 9 hours daily.
- Therefore, the total work can be calculated as:
- Total Work = 20 days * 9 hours/day = 180 hours.
- X's work capacity = 180 hours / 20 days = 9 hours/day.
- In 1 hour, X completes = 1/20 of the work.
Daily Work Contribution
- Day 1: Only X works.
- Work done = 5 hours * (1/180) = 1/36.
- Day 2: X + (2X) work together.
- Total capacity = (1 + 2) * (1/180) = 3/180.
- Work done = 5 hours * (3/180) = 1/12.
- Day 3: X + (2X) + (3X) work together.
- Total capacity = (1 + 2 + 3) * (1/180) = 6/180.
- Work done = 5 hours * (6/180) = 1/6.
- Day 4: X + (2X) + (3X) + (4X) work together.
- Total capacity = (1 + 2 + 3 + 4) * (1/180) = 10/180.
- Work done = 5 hours * (10/180) = 5/18.
Calculating Work Done Over Days
- Cumulative Work Calculation:
- End of Day 1: 1/36
- End of Day 2: 1/36 + 1/12 = 1/36 + 3/36 = 4/36 = 1/9
- End of Day 3: 1/9 + 1/6 = 1/9 + 2/18 = 1/9 + 4/36 = 7/36
- End of Day 4: 7/36 + 5/18 = 7/36 + 10/36 = 17/36
- Day 5:
- Work done = 15/180 = 1/12.
- Cumulative Work = 17/36 + 1/12 = 17/36 + 3/36 = 20/36 = 5/9.
- Day 6:
- Work done = 21/180 = 7/60.
- Cumulative Work = 5/9 + 7/60 = 50/90 + 14/90 = 64/90 = 32/45.
Completion of Work
- By Day 6, the work is nearing completion.
- On Day 7, with increasing capacity, the work will be completed.
Thus, the work will be completed on the 6th day.
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X can do a piece of work alone in 20 days, if he devotes 9 hours daily. However X works alone on the 1st day and on the 2nd day one man whose capacity to do the work is twice as that of X, joined in. On the 3rd day, another man whose capacity is thrice as that of X, joined and similarly on the 4th day, another man whose capacity is four times as that of X, joined them. The process continues this way until the work is completed. On which day will the work be completed, if everyone works for five hours a day?a)5th dayb)6th dayc)7th dayd)8th dayCorrect answer is option 'B'. Can you explain this answer?
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