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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?
- a)50
- b)89
- c)146
- d)175
Correct answer is option 'A,B,C,D'. 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...
Total man-hours per day = 125x7 = 875
Total man-hours in 39 days = 875x39 = 34125
Fraction of work complete = 5/7
The whole work needs = 7/5 x 34125 = 47775 man-hours
Remaining man-hours for the work to be completed = 47775-34125 = 13650
No. of days left = 52-39 = 13 days
Man-hours per day = 13650/13 = 1050
If each man works for 8hr /day, then no. of men = 1050/8 = 131.25 ≈ 132 men
No. of additional men = 132 - 125 = 7 men
7 men need to be added so as to complete the work on time.
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Total man-hours in 39 days = 875x39 = 34125
Fraction of work complete = 5/7
The whole work needs = 7/5 x 34125 = 47775 man-hours
Remaining man-hours for the work to be completed = 47775-34125 = 13650
No. of days left = 52-39 = 13 days
Man-hours per day = 13650/13 = 1050
If each man works for 8hr /day, then no. of men = 1050/8 = 131.25 ≈ 132 men
No. of additional men = 132 - 125 = 7 men
7 men need to be added so as to complete the work on time.
Most Upvoted Answer
A contract is to be completed in 52 days and 125 identical robots were...
Given information:
- Contract duration: 52 days
- Number of robots: 125
- Robots' operational hours per day: 7 hours
- Work completed after 39 days: 5/7 of the total work
- New operational hours per robot: 8 hours
Calculation:
Total work to be completed = 1 (100%)
Work completed after 39 days = 5/7
Remaining work = 1 - 5/7 = 2/7
Let's calculate the number of days required to complete the remaining work using the concept of man-days:
Total man-days required = Total work / Work done per day
Total work = Remaining work = 2/7
Work done per day = Number of robots * Operational hours per robot
For the initial 39 days, the robots were operational for 7 hours a day. So, the total work done per day = 125 * 7
For the remaining days, the robots will be operational for 8 hours a day. So, the total work done per day = (125 + X) * 8
Equating the total man-days required for both cases:
(2/7) / ((125 * 7) / 39) = (2/7) / ((125 + X) * 8) / (52 - 39)
Simplifying the equation:
39 * (125 * 7) = (52 - 39) * (125 + X) * 8
39 * 875 = 13 * (125 + X) * 8
(125 + X) * 8 = (39 * 875) / 13
125 + X = (39 * 875) / (13 * 8)
X = ((39 * 875) / (13 * 8)) - 125
Calculating the value of X:
X = (27375 / 104) - 125
X = 263.9423077 - 125
X ≈ 138.94
Therefore, approximately 139 additional robots would be required to complete the work on time.
Answer: Option A (139)
- Contract duration: 52 days
- Number of robots: 125
- Robots' operational hours per day: 7 hours
- Work completed after 39 days: 5/7 of the total work
- New operational hours per robot: 8 hours
Calculation:
Total work to be completed = 1 (100%)
Work completed after 39 days = 5/7
Remaining work = 1 - 5/7 = 2/7
Let's calculate the number of days required to complete the remaining work using the concept of man-days:
Total man-days required = Total work / Work done per day
Total work = Remaining work = 2/7
Work done per day = Number of robots * Operational hours per robot
For the initial 39 days, the robots were operational for 7 hours a day. So, the total work done per day = 125 * 7
For the remaining days, the robots will be operational for 8 hours a day. So, the total work done per day = (125 + X) * 8
Equating the total man-days required for both cases:
(2/7) / ((125 * 7) / 39) = (2/7) / ((125 + X) * 8) / (52 - 39)
Simplifying the equation:
39 * (125 * 7) = (52 - 39) * (125 + X) * 8
39 * 875 = 13 * (125 + X) * 8
(125 + X) * 8 = (39 * 875) / 13
125 + X = (39 * 875) / (13 * 8)
X = ((39 * 875) / (13 * 8)) - 125
Calculating the value of X:
X = (27375 / 104) - 125
X = 263.9423077 - 125
X ≈ 138.94
Therefore, approximately 139 additional robots would be required to complete the work on time.
Answer: Option A (139)
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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?a)50b)89c)146d)175Correct answer is option 'A,B,C,D'. Can you explain this answer?
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