Pipes and Cisterns – Open both taps briefly, then continue with the slower tap: A tank can be filled by tap 1 in 20 minutes and by tap 2 in 60 minutes. Both taps are opened for 5 minutes, after which tap 1 is closed. How much additional time will it take for the tank to be completely filled?

Introduction / Context:
We handle this in two phases: the first 5 minutes with both taps, then the remaining fraction with just the slower tap. Using rates ensures exact accounting of the filled fraction.

Given Data / Assumptions:

• Tap 1: 20 min ⇒ 1/20 per min.
• Tap 2: 60 min ⇒ 1/60 per min.
• Phase 1 duration = 5 min with both; Phase 2 is only tap 2.

Concept / Approach:
Compute the fraction filled in the first 5 minutes, subtract from 1, then divide the remainder by tap 2’s rate.

Step-by-Step Solution:
In 5 min: fraction = 5*(1/20 + 1/60) = 5*( (3 + 1)/60 ) = 5*(4/60) = 1/3.Remaining = 1 − 1/3 = 2/3.Tap 2 alone rate = 1/60 ⇒ remaining time = (2/3) / (1/60) = 40 min.

Verification / Alternative check:
Equivalent total time = 5 + 40 = 45 min overall, but the question asks for the time after closing tap 1, i.e., 40 min.

Why Other Options Are Wrong:
20, 30, 35, 45 minutes correspond to misreading the question or miscomputing the first 5-minute contribution.

Common Pitfalls:
Answering with 45 min (total) rather than the requested additional time after closing tap 1.

Final Answer:
40 min