Explanation:

Let’s break down the problem:

- Pipe P’s rate: fills 1/24 of the tank per minute.

- Pipe Q’s rate: fills 1/36 of the tank per minute.

- Pipe R’s rate: empties 1/30 of the tank per minute.

- When all pipes are open: Net rate = (1/24) + (1/36) - (1/30) = (15 + 10 - 12)/(360) = 13/360 per minute.

- Let Q be closed after x minutes:

- In x minutes, (13/360) × x tank is filled.

- After that, only P and R work: net rate = (1/24) - (1/30) = (5-4)/120 = 1/120 per minute.

- Time after closing Q = 60 - x minutes.

- Amount filled in this period = (60-x)×(1/120)

- Sum total to fill the tank:

(13x/360) + ((60-x)/120) = 1

Simplify:

(13x/360) + (60/120 - x/120) = 1

(13x/360) + (1/2 - x/120) = 1

Get common denominator:

(13x/360) - (3x/360) = 1 - 1/2

(10x/360) = 1/2

(x/36) = 1/2

x = 18 minutes

Here’s the options analysis:

- Option 1: 18 ? Correct Answer

- Option 2: 15

- Option 3: 24

- Option 4: 30

Key Points:

- The answer is ? Q should be closed after 18 min for the tank to be filled in 1 hour.

- Only option 1 fits the correct calculation.

- Double-check the set-up: all rates, net contributions, and total requirement.

Correct Answer: Option 1 (18 minutes)