Question

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 ______.

Options

• 3 hrs

• 6 hrs

• 1 hr

• 5 hrs

Answer 1

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 6 hrs.

Explanation:

Time taken by second pipe to fill the cistern above = x hrs

∴ Time taken by first pipe to fill the cistern alone = (x – 3) hrs

∴ First pipe alone one hrs work = `1/(x - 3)`

Second pipe alone one hrs work = `1/x`

Thus, both pipes together's one hrs work = `1/(x - 3) + 1/x`

∴ `1/(x - 3) + 1/x = 1/2`

`\implies (x + x - 3)/(x(x - 3)) = 1/2`

`\implies (2x - 3)/(x(x - 3)) = 1/2`

`\implies` 2(2x – 3) = x(x – 3)

`\implies` 4x – 6 = x² – 3x

`\implies` x² – 3x – 4x + 6 = 0

`\implies` x² – 7x + 6 = 0

`\implies` x² – 6x – x + 6 = 0

`\implies` x(x – 6) – 1(x – 6) = 0

`\implies` (x – 6)(x – 1) = 0

Either x – 6 = 0 or x – 1 = 0

`\implies` x = 6 or 1

∴ x = 6

When x = 1 then the time taken by first pipe is negative further both pipes together fill the cistern in 2 hrs.