Question

Two pipes running together can fill a tank in 100/9 minutes. If one pipe takes 5 minutes
more than the other to fill the tank separately, find the time in which each pipe would fill
the tank separately.​

Answer 1

Answer:

20 and 25 minutes respectively.

Step-by-step explanation:

Let there be two pipes, A and B.

• A takes more time i.e., 5 mins more than B to fill tank separately.

Let time taken by B be x mins. Then time taken by A will be x + 5 mins.

→ 100/(9x) + 100/[9(x + 5)] = 1

→ 100/9 × (1/x) + 100/9 × 1/(x + 5) = 1

→ 1/x + 1/(x + 5) = 9/100

→ (x + 5 + x)/(x² + 5x) = 9/100

→ 100(2x + 5) = 9(x² + 5x)

→ 200x + 500 = 9x² + 45x

→ 9x² - 155x - 500 = 0

• D = b² - 4ac
• D = (-155)² - 4(9)(-500)
• D = 42025

Now, x = (- b ± √D)/2a

→ x = (155 ± √42025)/2(9)

→ x = (155 ± 205)/18

Case 1: When it's + 205,

→ x = (155 + 205)/18

→ x = 20

Case 2: When it's - 205,

→ x = (155 - 205)/18

→ x = - 50/18

“Since time can't be negative hence, value of x is 20 mins.”

• Time taken by B = 20 mins

• Time taken by A = 20 + 5 = 25 mins

To fill tank separately.