Two pipes flowing together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.

Smrutirekha Pathak · 18th Feb 2019 .

Raja Swain · 18th Feb 2019 .

Let the time taken by the two pipes to fill the cistern be x and x + 5 min. respectively.

In 1 min., the first pipe can fill 1/x of the cistern. In 1 min., the second pipe can fill 1/x + 5 of the cistern then

1/x + 1/x + 5 = 1/6

⇒ x + 5 + x/x(x + 5) = 1/6

⇒ 2x + 5/x2 + 5x = 1/6

⇒ x2 + 5x = 12x + 30

⇒ x2 – 7x – 30 = 0

⇒ x2 – 10x + 3x – 30 = 0

⇒ x(x – 10) + 3(x – 10) = 0

⇒ (x – 10)(x + 3) = 0

⇒ x – 10 = 0 or x = - 3

⇒ x = 10 or x = - 3

Since, time can not be negative.

So, x = 10 and x + 5 = 10 + 5 = 15

Jasmita Das · 16th Mar 2019 .

Let total work done by two pipes in one minute is 1/6.

One of them done in one minute is 1/x & another one done it in one minute is 1/(x+5).

So that

1/x + 1/(x+5) = 1/6

After solving this...

x=10...

x+5=15

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