Question : P can fill a tank in 5 hours, and Q can fill the same tank in 10 hours. R can empty the same tank in 20 hours. How much time will all the three take together to fill the same tank?
Option 1: 10 hours
Option 2: 4 hours
Option 3: 6 hours
Option 4: 5 hours
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Correct Answer: 4 hours
Solution :
P can fill a tank in 5 hours.
Q can fill the same tank in 10 hours.
R can empty the same tank in 20 hours.
P's per hour efficiency = $\frac{1}{5}$
Q's per hour efficiency = $\frac{1}{10}$
R's per hour efficiency = $- \frac{1}{20}$ (negative because it is emptying the tank)
Total efficiency of P, Q, and R working together = $\frac{1}{5} + \frac{1}{10} − \frac{1}{20}$ = $\frac{5}{20}$ = $\frac{1}{4}$
$\therefore$ Together they will take 4 hours to fill the tank.
Hence, the correct answer is 4 hours.
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