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A cistern has 2 pipes, 1 can fill with water in 16 hours and other can empty it in 10 hours. in how many hours will the cistern be emptied if both the pipes are opened together when 1/5th of the cistern is already filled with water? The Correct answer is 5.33 hours
A cistern has 2 pipes, 1 can fill with water in 16 hours and other can empty it in 10 hours. in how many hours will the cistern be emptied if both the pipes are opened together when 1/5th of the cistern is already filled with water?
The Correct answer is 5.33 hours
Explanation
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Rate of filling for the first pipe (in cisterns per hour) = 1/16 (since it fills the cistern in 16 hours)
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Rate of emptying for the second pipe (in cisterns per hour) = 1/10 (since it empties the cistern in 10 hours)
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Fraction of the cistern already filled = 1/5
When both pipes are open together, their combined rate is: Combined rate = Rate of filling for the first pipe – Rate of emptying for the second pipe
Combined rate = 1/16 – 1/10
Combined rate = (5 – 8) / 80
Combined rate = -3 / 80
This means that the cistern is being emptied at a rate of 3/80 cisterns per hour when both pipes are open together.
Since 1/5th of the cistern is already filled, 4/5th of the cistern needs to be emptied.
Time taken to empty 4/5th of the cistern: Time = (Volume to be emptied) / (Rate of emptying)
Time = (4/5) / (3/80) Time = (4/5) * (80/3)
Time = 16/3 Time ≈ 5.33 hours
What is the Combined rate?
In mathematics, a combined rate is a single rate that represents the total effect of multiple rates acting together. It is often used in problems involving compound interest, where different interest rates are applied to different parts of a principal amount.
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For example, suppose you have an investment that earns 5% interest annually for the first three years and then earns 3% interest annually for the next two years. The combined rate for the entire five-year period would be the rate that would give you the same total amount of interest if it were applied to the entire principal for the entire five years.
To calculate the combined rate, you would typically use a formula that takes into account the different rates and the times they are applied. This formula varies depending on the specific scenario, but it generally involves weighted averages of the individual rates.
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Categories: Math
