Pipes A and B fill a tanker in 60 min and 40 min. B is used for half the total time; A and B together fill for the other half. How many minutes to fill the tanker?

Problem restatement
Let total time be T minutes. For T/2 minutes only B runs; for T/2 minutes A and B run together. Find T so that 1 full tank is filled.

Given data

• Rate(A) = 1/60 tank/min; Rate(B) = 1/40 tank/min.
• Rate(A + B) = 1/60 + 1/40 = 1/24 tank/min.

Concept/Approach
Total work = (time × rate) summed over phases; set equal to 1.

Step-by-step calculation
Work = (T/2)×(1/40) + (T/2)×(1/24) = T×(1/80 + 1/48) 1/80 + 1/48 = (3/240 + 5/240) = 8/240 = 1/30 Thus T × (1/30) = 1 ⇒ T = 30 minutes

Verification/Alternative
In 15 min, B alone fills 15/40 = 0.375; in next 15 min, A+B fill 15/24 = 0.625; total = 1.000 (exact).

Common pitfalls

• Assuming sequential halves mean equal work instead of equal time.

Final Answer
30 minutes