Q. 1
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A tap fills a tank in eight hours. Two taps at the bottom of the tank can empty it in 15 and 20 hours respectively. If all the three taps are opened simultaneously, the tank will be full in __ hours.
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Step-by-Step Explanation & Concept Rationale
Here is the step-by-step breakdown using the net work per hour approach:
Inlet rate (filling): \(\frac{1}{8}\) of the tank per hour.
First outlet rate (emptying): \(-\frac{1}{15}\) of the tank per hour.
Second outlet rate (emptying): \(-\frac{1}{20}\) of the tank per hour.
Net work done in 1 hour:\(\frac{1}{8}-\frac{1}{15}-\frac{1}{20}\)
Find the Least Common Multiple (LCM): The LCM of 8, 15, and 20 is 120.
Calculate the net rate:
\(\frac{15-8-6}{120}=\frac{1}{120}\)
Since \(\frac{1}{120}\) of the tank is filled every hour, it will take exactly 120 hours to fill the tank completely.
Inlet rate (filling): \(\frac{1}{8}\) of the tank per hour.
First outlet rate (emptying): \(-\frac{1}{15}\) of the tank per hour.
Second outlet rate (emptying): \(-\frac{1}{20}\) of the tank per hour.
Net work done in 1 hour:\(\frac{1}{8}-\frac{1}{15}-\frac{1}{20}\)
Find the Least Common Multiple (LCM): The LCM of 8, 15, and 20 is 120.
Calculate the net rate:
\(\frac{15-8-6}{120}=\frac{1}{120}\)
Since \(\frac{1}{120}\) of the tank is filled every hour, it will take exactly 120 hours to fill the tank completely.
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