Two pipes running 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.

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10 min, 13min

14 min, 15min

10 min,15 min

20 min, 25 min

answer is D.

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Detailed Solution

It is given that two pipes running together can fill a tank in 6 minutes.
If one pipe takes 5 minutes more than the other pipe to fill the tank separately.
Let us assume that the time taken by the two pipes to fill the cistern be

x min

and

x + 5 m i n

respectively.
Since, two pipes running together can fill a tank in 6 minutes.
Thus,

⇒ 1 x + 1 x + 5 = 16 ⇒ x + 5 + x x (x + 5) = 16 ⇒ x 2 + 5 x = 12 x + 30 ⇒ x 2 − 7 x − 30 = 0

Then,

⇒ x 2 − 10 x + 3 x − 30 = 0 ⇒ x (x − 10) + 3 (x − 10) = 0 ⇒ (x + 3) (x − 10) = 0 ⇒ x = 10, − 3

Neglecting the negative value, we get the value of x to be 10 min.
Thus, the time taken by the other pipe is,

= x + 5 = 10 + 5 = 15 min

The time taken by each pipe to fill the tank is 10 minutes and 15 minutes respectively.
Hence, the correct option is 4.

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