Pipes A and B fill a cistern in 37½ min and 45 min. If both open together but B is closed after some time, the cistern just fills in 30 min. After how many minutes should B be closed?

Problem restatement
Run A and B together for t minutes, then only A runs, so that total fill time is 30 minutes.

Given data

• A's time = 37.5 min ⇒ rate A = 2/75 per min
• B's time = 45 min ⇒ rate B = 1/45 per min
• Total time = 30 min

Concept/Approach
Work equation: t(A+B) + (30 − t)A = 1 tank ⇒ 30A + tB = 1.

Step-by-step calculation
30A = 30 × (2/75) = 4/5 = 0.8tB = 1 − 0.8 = 0.2t = 0.2 / (1/45) = 9Close B after 9 minutes

Verification/Alternative
First 9 min: work = 9(2/75 + 1/45) = 9( (6 + 5)/225 ) = 9(11/225) = 99/225 = 0.44. Remaining 21 min by A: 21 × 2/75 = 42/75 = 0.56. Total = 1.

Common pitfalls
Using 37.5 as 37 or 38; keep it as 75/2 to avoid rounding.

Final Answer
9 minutes