Pipe A alone can fill a tank in 24 minutes. Pipe B alone can fill the same tank in 36 minutes. Pipe A alone is opened for x minutes and Pipe B alone is opened for y minutes to fill the tank in 30 minutes. Then |x - y| = (in minutes)

Given:

Pipe A can fill the tank in 24 minutes.

Pipe B can fill the tank in 36 minutes.

Total time to fill the tank = 30 minutes.

Pipe A works for x minutes and Pipe B works for y minutes.

We need to find |x - y|.

Formula used:

Work done = Rate × Time

Rate of Pipe A = 1/24 tanks per minute

Rate of Pipe B = 1/36 tanks per minute

Total work = 1 tank

Work done by Pipe A + Work done by Pipe B = Total work

Work done by Pipe A = (1/24) × x

Work done by Pipe B = (1/36) × y

Calculation:

(1/24) × x + (1/36) × y = 1

⇒ Multiply through by LCM (24 × 36 = 864)

⇒ 864 × (1/24) × x + 864 × (1/36) × y = 864 × 1

⇒ 36x + 24y = 864

⇒ Divide through by 12

⇒ 3x + 2y = 72

Also, x + y = 30 (total time)

⇒ 2 equations:

1) 3x + 2y = 72

2) x + y = 30

From equation 2:

⇒ y = 30 - x

Substitute y = 30 - x into equation 1:

⇒ 3x + 2(30 - x) = 72

⇒ 3x + 60 - 2x = 72

⇒ x = 12

Substitute x = 12 into equation 2:

⇒ y = 30 - 12

⇒ y = 18

|x - y| = |12 - 18|

⇒ |x - y| = 6

∴ The correct answer is option (4).