Discussion
Which of the following statements is/are correct?
1. Pipe X can fill a tank in 30 hr. and pipe Y in 45 hr. If both the pipes are opened to fill an empty tank, then the tank will get filled in 8 hrs.
2. Two pipes P and Q can fill a tank in 15 hr. and 20 hr. respectively while a third pipe R can empty the full tank in 25 hr. All the three pipes are opened together. After 10 hr. R is closed. The tank will be full in next 12 hr.
Select the answer using the code given below:
Answer: D
Neither 1 nor 2 is correct.
Statement 1: together X and Y fill \(\tfrac{1}{30} + \tfrac{1}{45} = \tfrac{5}{90} = \tfrac{1}{18}\) of the tank an hour, so they need 18 hours, not 8.
Statement 2: with all three open the net rate is
\[ \begin{aligned} \tfrac{1}{15} + \tfrac{1}{20} - \tfrac{1}{25} &= \tfrac{20 + 15 - 12}{300} = \tfrac{23}{300} \\ 10 \text{ h} &\to \tfrac{230}{300} \text{ filled} \end{aligned} \]
The remaining \(\tfrac{70}{300}\) is filled by P and Q at \(\tfrac{35}{300}\) an hour in 2 hours, not 12. Both statements are false.
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