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A contract is to be completed in 52 days and 125 identical robots were employed, each
operational for 7 hours a day. After 39 days, five-seventh of the work was completed.
How many additional robots would be required to complete the work on time, if each
robot is now operational for 8 hours a day?
operational for 7 hours a day. After 39 days, five-seventh of the work was completed.
How many additional robots would be required to complete the work on time, if each
robot is now operational for 8 hours a day?
- a)5
- b)8
- c)7
- d)14
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A contract is to be completed in 52 days and 125 identical robots were...
Additional robots required = 131.25 − 125 = 6.25 ≈ 7
Most Upvoted Answer
A contract is to be completed in 52 days and 125 identical robots were...
Work Calculation Overview
To determine how many additional robots are required, we first need to analyze the work done and remaining work.
Initial Work Done
- Total work is represented as 1 (or 100%).
- After 39 days, five-sevenths of the work is completed:
- Work completed = 5/7
- Remaining work = 1 - 5/7 = 2/7
Time Remaining
- Total duration of the contract = 52 days
- Days elapsed = 39 days
- Days remaining = 52 - 39 = 13 days
Total Work Rate of Current Robots
- Number of robots = 125
- Each robot operates for 7 hours a day, so total hours worked in 39 days:
- Total hours = 125 robots * 7 hours/day * 39 days = 34,125 hours
- Work done in terms of hours = 5/7 of total work
Work Rate Calculation
- Work rate = Total hours worked / Work done = 34,125 / (5/7) = 47,775 hours (Total work in hours)
Remaining Work Requirement
- Remaining work = 2/7 of total work
- Hours needed for remaining work = 47,775 * (2/7) = 13,393.57 hours
Required Work Rate for Remaining Time
- Time remaining = 13 days * 8 hours/day = 104 hours (new operational hours)
- Required work rate = Remaining hours / Remaining days = 13,393.57 / 104 = 128.5 robots
Calculating Additional Robots
- Current robots = 125
- Additional robots needed = 128.5 - 125 = 3.5 (round up to 4)
Thus, to meet the deadline, you need 4 additional robots. However, you specified option 'C' (7) as the correct answer, which could imply a revision of calculations or assumptions. Please review specifics regarding hours or work done if needed.
To determine how many additional robots are required, we first need to analyze the work done and remaining work.
Initial Work Done
- Total work is represented as 1 (or 100%).
- After 39 days, five-sevenths of the work is completed:
- Work completed = 5/7
- Remaining work = 1 - 5/7 = 2/7
Time Remaining
- Total duration of the contract = 52 days
- Days elapsed = 39 days
- Days remaining = 52 - 39 = 13 days
Total Work Rate of Current Robots
- Number of robots = 125
- Each robot operates for 7 hours a day, so total hours worked in 39 days:
- Total hours = 125 robots * 7 hours/day * 39 days = 34,125 hours
- Work done in terms of hours = 5/7 of total work
Work Rate Calculation
- Work rate = Total hours worked / Work done = 34,125 / (5/7) = 47,775 hours (Total work in hours)
Remaining Work Requirement
- Remaining work = 2/7 of total work
- Hours needed for remaining work = 47,775 * (2/7) = 13,393.57 hours
Required Work Rate for Remaining Time
- Time remaining = 13 days * 8 hours/day = 104 hours (new operational hours)
- Required work rate = Remaining hours / Remaining days = 13,393.57 / 104 = 128.5 robots
Calculating Additional Robots
- Current robots = 125
- Additional robots needed = 128.5 - 125 = 3.5 (round up to 4)
Thus, to meet the deadline, you need 4 additional robots. However, you specified option 'C' (7) as the correct answer, which could imply a revision of calculations or assumptions. Please review specifics regarding hours or work done if needed.
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