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A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?
- a)35 hours
- b)30 hours
- c)28 hours
- d)20 hours
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A reservoir will be filled in 12 hours if two pipes function simultan...
Problem Overview
A reservoir can be filled in 12 hours when two pipes operate together. The second pipe is 10 hours faster than the first in filling the reservoir. We need to determine how long the second pipe takes to fill the reservoir.
Let’s Define the Variables
- Let the time taken by the first pipe be T hours.
- Therefore, the second pipe will take (T - 10) hours.
Rate of Filling
- The rate of the first pipe is 1/T (reservoirs per hour).
- The rate of the second pipe is 1/(T - 10) (reservoirs per hour).
Combined Rate
When both pipes work together:
- Combined rate = Rate of first pipe + Rate of second pipe
- Combined rate = 1/T + 1/(T - 10)
Since they fill the reservoir in 12 hours together:
- Combined rate = 1/12
Thus, we can set up the equation:
1/T + 1/(T - 10) = 1/12
Finding a Common Denominator
The common denominator for T and (T - 10) is T(T - 10):
- (T - 10 + T) / (T(T - 10)) = 1/12
Simplifying the Equation
This simplifies to:
- (2T - 10) = T(T - 10)/12
Cross-multiplying gives:
- 12(2T - 10) = T^2 - 10T
Resulting in:
- T^2 - 34T + 120 = 0
Solving the Quadratic Equation
Applying the quadratic formula:
- T = (34 ± √(34^2 - 4*1*120)) / (2*1)
Calculating the discriminant and solving yields T = 30 hours for the first pipe.
Time for the Second Pipe
Thus, the time taken by the second pipe is:
- T - 10 = 30 - 10 = 20 hours.
Conclusion
The second pipe will take 20 hours to fill the reservoir, confirming option 'D'.
A reservoir can be filled in 12 hours when two pipes operate together. The second pipe is 10 hours faster than the first in filling the reservoir. We need to determine how long the second pipe takes to fill the reservoir.
Let’s Define the Variables
- Let the time taken by the first pipe be T hours.
- Therefore, the second pipe will take (T - 10) hours.
Rate of Filling
- The rate of the first pipe is 1/T (reservoirs per hour).
- The rate of the second pipe is 1/(T - 10) (reservoirs per hour).
Combined Rate
When both pipes work together:
- Combined rate = Rate of first pipe + Rate of second pipe
- Combined rate = 1/T + 1/(T - 10)
Since they fill the reservoir in 12 hours together:
- Combined rate = 1/12
Thus, we can set up the equation:
1/T + 1/(T - 10) = 1/12
Finding a Common Denominator
The common denominator for T and (T - 10) is T(T - 10):
- (T - 10 + T) / (T(T - 10)) = 1/12
Simplifying the Equation
This simplifies to:
- (2T - 10) = T(T - 10)/12
Cross-multiplying gives:
- 12(2T - 10) = T^2 - 10T
Resulting in:
- T^2 - 34T + 120 = 0
Solving the Quadratic Equation
Applying the quadratic formula:
- T = (34 ± √(34^2 - 4*1*120)) / (2*1)
Calculating the discriminant and solving yields T = 30 hours for the first pipe.
Time for the Second Pipe
Thus, the time taken by the second pipe is:
- T - 10 = 30 - 10 = 20 hours.
Conclusion
The second pipe will take 20 hours to fill the reservoir, confirming option 'D'.
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Community Answer
A reservoir will be filled in 12 hours if two pipes function simultan...
Let the first pipe fill the reservoir in x hours.
Then, the second pipe can fill the reservoir in x – 10 hours.
Now, according to the question,
1/x + 1/x-10 = 1/12
⇒ 12(x – 10 + x) = x2 – 10x
⇒ 24x – 120 = x2 – 10x
⇒ x2 – 34x + 120 = 0
⇒ x2 – 30x - 4x + 120 = 0
⇒ (x – 30)(x – 4) = 0
⇒ x = 30, 4
But, x ≠ 4 (∵ x – 10 should be positive)
∴ x = 30 hours
x – 10 = 20 hours
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Question Description
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A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?a)35 hoursb)30 hoursc)28 hoursd)20 hoursCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2026 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?a)35 hoursb)30 hoursc)28 hoursd)20 hoursCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A reservoir will be filled in 12 hours if two pipes function simultaneously. The second pipe fills the reservoir 10 hours faster than the first. How many hours will the second pipe take to fill the reservoir?a)35 hoursb)30 hoursc)28 hoursd)20 hoursCorrect answer is option 'D'. Can you explain this answer?.
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