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12 pumps working 6 hours a day can empty a completely filled reservoir in 15 days. How many such pumps working 9 hours a day will empty the same reservoir in 12 days ?
- a)12
- b)15
- c)9
- d)10
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
12 pumps working 6 hours a day can empty a completely filled reservoir...
Let x be number of pumps
9 : 6 : : 12 : x = 12 : 15 : : 12 : x
9 × 12 × x = 6 × 12 × 15
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Community Answer
12 pumps working 6 hours a day can empty a completely filled reservoir...
Understanding the Problem
We have 12 pumps that can empty a reservoir in 15 days, working 6 hours a day. We need to find out how many pumps are required to empty the same reservoir in 12 days, working 9 hours a day.
Calculating Total Work Done
- The total work done (in pump-hours) can be calculated as:
Total work = Number of pumps × Hours per day × Days
- For the initial setup:
Total work = 12 pumps × 6 hours/day × 15 days = 1080 pump-hours
Calculating New Requirements
- We need to empty the same reservoir in 12 days with pumps working 9 hours a day.
- Let the number of pumps needed be 'x'.
- The total work in this case will be:
Total work = x pumps × 9 hours/day × 12 days = 108x pump-hours
Setting Equations Equal
- Since both scenarios empty the same reservoir, we can set the total work equal:
1080 pump-hours = 108x pump-hours
Solving for x
- To find x, we rearrange the equation:
x = 1080 / 108 = 10
Conclusion
- Therefore, 10 pumps working 9 hours a day will empty the reservoir in 12 days.
The correct answer is option 'D' (10).
We have 12 pumps that can empty a reservoir in 15 days, working 6 hours a day. We need to find out how many pumps are required to empty the same reservoir in 12 days, working 9 hours a day.
Calculating Total Work Done
- The total work done (in pump-hours) can be calculated as:
Total work = Number of pumps × Hours per day × Days
- For the initial setup:
Total work = 12 pumps × 6 hours/day × 15 days = 1080 pump-hours
Calculating New Requirements
- We need to empty the same reservoir in 12 days with pumps working 9 hours a day.
- Let the number of pumps needed be 'x'.
- The total work in this case will be:
Total work = x pumps × 9 hours/day × 12 days = 108x pump-hours
Setting Equations Equal
- Since both scenarios empty the same reservoir, we can set the total work equal:
1080 pump-hours = 108x pump-hours
Solving for x
- To find x, we rearrange the equation:
x = 1080 / 108 = 10
Conclusion
- Therefore, 10 pumps working 9 hours a day will empty the reservoir in 12 days.
The correct answer is option 'D' (10).
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