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प्रश्न
One pipe can fill a cistern in 3 hours less than the other. The two pipes together can fill the cistern in 6 hours 40 minutes. Find the time that each pipe will take to fill the cistern.
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उत्तर
Let one pipe fill the cistern in x hours and the other fills it in (x – 3) hours.
Given that the two pipes together can fill the cistern in 6 hours 40 minutes,
i.e., `6 40/60 "hours" = 6 2/3 "hour" = 20/3 "hours"`
`1/x + 1/(x - 3) = 3/20`
`(x - 3 + x)/(x(x - 3)) = 3/20`
`(2x - 3)/(x^2 - 3x) = 3/20`
`40x - 60 = 3x^2 - 9x`
`3x^2 - 49x + 60 = 0`
`3x^2 - 45x - 4x + 60 = 0`
`3x(x - 15) - 4(x - 15) = 0`
`(x - 15)(3x - 4) = 0`
`x = 15, 4/3`
If `x = 4/3`,
Then `x - 3 = 4/3 - 3`
= `(4- 9)/3`
= `(-5)/3`,
Which is not possible
So, x = 15
Thus, one pipe fill the cistern in 15 hours and other fills in (x – 3) = 15 – 3 = 12 hours.
संबंधित प्रश्न
A can do a piece of work in ‘x’ days and B can do the same work in (x + 16) days. If both working together can do it in 15 days. Calculate ‘x’.
A can do a piece of work in 5 days and B can do the same work in (x + 5) days. The total number of days taken by A and B, working together, is `3 1/3`. The value of x is ______.
One pipe can fill an empty cistern in 3 hrs less than the another pipe. When both the pipes are opened together, the empty cistern is filled in 2 hrs. The second pipe will fill the empty cistern in ______.
