Q. 1
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Pipe A can fill a tank in 25 minutes and Pipe B can fill it in 30 minutes. Both pipes are opened together, but Pipe A is turned off after some time and Pipe B finishes filling the tank in $16\frac{4}{5}$ minutes more. After how many minutes was Pipe A turned off?
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Step-by-Step Explanation & Concept Rationale
Pipe B alone filled for $16\frac{4}{5} = \frac{84}{5}\text{ minutes}$: \[\text{Work done by B} = \frac{84}{5} \times \frac{1}{30} = \frac{84}{150} = \frac{14}{25}\] Remaining work filled by both A and B together: \[1 - \frac{14}{25} = \frac{11}{25}\] Combined filling rate of A and B: \[\frac{1}{25} + \frac{1}{30} = \frac{6 + 5}{150} = \frac{11}{150}\] Time both pipes were open together: \[\text{Time} = \frac{11/25}{11/150} = \frac{11}{25} \times \frac{150}{11} = 6\text{ minutes}\] Thus, Pipe A was turned off after 6 minutes. Thus, the correct option is (B).
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