Miscellaneous Question 76
- There are 3 inlet pipes $X, Y$ and $Z$ connected to a tank. If only one pipe is opened at a time, then it takes 50, 40 and 25 minutes for pipes $X, Y$ and $Z$ respectively to fill the tank. Find the time taken to fill $99 \%$ of the tank if it is known that in every 5 minutes for the first 2 minutes pipe $Y$ is opened and then closed for 3 minutes. The remaining pipes are always kept open. (In minutes)
(1) 15
(2) 16
(3) 12
(4) 14
(5) 11
IBPS RRBs Officer CWE (Prelim Exam) 17.08.2019
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Correct Answer: 76. (4)
Solution: 76. (4) Part of tank filled by all three pipes in first 5 minutes
$=\frac{5}{50}+\frac{2}{40}+\frac{5}{25}$ $=\frac{1}{10}+\frac{1}{20}+\frac{1}{5}$
$=\frac{2+1+4}{20}=\frac{7}{20}$
$\therefore \quad$ Part filled in first 10 minutes
$=\frac{14}{20}=\frac{7}{10}$
Remaining part $=1-\frac{7}{10}=\frac{3}{10}$
Part of tank filled by all three inlets in the next 4 minutes
$=\frac{4}{50}+\frac{2}{40}+\frac{4}{25}$
$=\frac{16+10+32}{200}=\frac{58}{200}=\frac{29}{100}$
i.e., $99 \%$ part will be filled in 11 minutes
$\because \quad \frac{29}{100}+\frac{7}{10}=\frac{99}{100}$
BETA
