During rainy season, huge inflow of water takes place into a reservoir. Measures are taken to clear the reservoir while water keeps flowing into it at a constant rate. It has been observed that seven and five men can clear the reservoir in 20 and 50 days, respectively, with the initial quantity of water in the reservoir being 24 and 36 kilolitres, respectively. What is the rate of inflow of water into the reservoir in litres per day?
To find the rate of inflow of water into the reservoir, we can first calculate the rates at which the men can clear the reservoir.
Let's denote the rate of work of seven men as M1 and the rate of work of five men as M2.
From the given information, we know that:
M1 * 20 = 24 (equation 1)
M2 * 50 = 36 (equation 2)
Now, let's solve these equations to find the rates of work:
From equation 1, we can solve for M1:
M1 = 24 / 20 = 1.2 kilolitres per day
From equation 2, we can solve for M2:
M2 = 36 / 50 = 0.72 kilolitres per day
Now, let's consider the rate of inflow of water into the reservoir as R. Since the men are continuously clearing the reservoir while the water is flowing in, the net rate of water flowing into the reservoir should be zero.
In other words, the rate at which water is flowing into the reservoir (R) is equal to the combined rate at which the men are clearing the reservoir (M1 + M2):
R = M1 + M2
R = 1.2 + 0.72
R = 1.92 kilolitres per day
Finally, we need to convert the rate of inflow from kilolitres to litres. Since 1 kilolitre is equal to 1000 litres, we multiply the rate by 1000:
R = 1.92 * 1000 = 1920 litres per day
Therefore, the rate of inflow of water into the reservoir is 1920 litres per day.
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To find the rate of inflow of water into the reservoir in liters per day, we need to analyze the information given and apply some mathematical calculations.
Let's start by assigning variables to the unknown quantities. Let's call the rate of inflow of water "R" liters per day.
According to the problem, seven men can clear the reservoir in 20 days with an initial quantity of water in the reservoir being 24 kiloliters. This means that the work done by the seven men is the same as the water inflow during these 20 days. We can represent this relationship mathematically as:
7 * 20 = 24 * 1000 * R
Simplifying this equation, we have:
R = (7 * 20) / (24 * 1000)
R = 0.05833 kiloliters per day
Similarly, we can do the same calculations for five men clearing the reservoir in 50 days with an initial quantity of water in the reservoir being 36 kiloliters:
5 * 50 = 36 * 1000 * R
R = (5 * 50) / (36 * 1000)
R = 0.06944 kiloliters per day
Now, to convert kiloliters to liters, we multiply both of these results by 1000:
0.05833 kiloliters/day * 1000 = 58.33 liters/day
0.06944 kiloliters/day * 1000 = 69.44 liters/day
Therefore, the rate of inflow of water into the reservoir is approximately 58.33 liters per day or 69.44 liters per day, depending on whether seven or five men are clearing the reservoir.
Note: The rate of inflow may vary depending on the number of men working to clear the reservoir.
assuming each man can x liters/day, then if the inflow rate is y liters/day, we have
24000+20(y - 7x) = 0
36000+50(y - 5x) = 0
x = 240
y = 280