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Question : Two inlet pipes can fill a cistern in 10 and 12 hours respectively and an outlet pipe can empty 80 gallons of water per hour. All three pipes working together can fill the empty cistern in 20 hours. What is the capacity (in gallons) of the tank?

Option 1: 360

Option 2: 300

Option 3: 600

Option 4: 900


Team Careers360 2nd Jan, 2024
Answer (1)
Team Careers360 13th Jan, 2024

Correct Answer: 600


Solution : Let the time taken by the outlet pipe to empty the tank be $x$ hour.
One hour's work of pipe A = $\frac{1}{10}$
One hour's work of pipe B = $\frac{1}{12}$
One hour's work of pipe C = $-\frac{1}{x}$
When all pipes work together, the tank will be emptied in 20 hours.
So, $\frac{1}{10}+\frac{1}{12}-\frac{1}{x} =\frac{1}{20}$
⇒$\frac{1}{10}+\frac{1}{12}-\frac{1}{20} =\frac{1}{x}$
⇒$\frac{1}{x}=\frac{6+5-3}{60}$
⇒$\frac{1}{x}=\frac{8}{60}$
$\therefore x = \frac{15}{2}=7.5$
Therefore, the outlet pipe can empty the tank in 7.5 hours.
In one hour, it empties 80 gallons.
In 7.5 hours, it empties 80 × 7.5 = 600 gallons
So, the capacity of the tank is 600 gallons.
Hence, the correct answer is 600.

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