Pipes and Cisterns - Basic Formulas, Shortcuts, Rules, Tricks & Tips - Quantitative Aptitude

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Pipes and Cisterns is a common topic in Quantitative Aptitude which involves questions related to the filling or emptying of tanks, cisterns, or pipes. Here are some basic formulas, shortcuts, rules, tricks, and tips for solving Pipes and Cisterns problems:

Work formula: Work = (time × rate) If a pipe can fill a tank in 'x' hours, then the rate of filling the tank is $1/x$. If a pipe can empty a tank in 'y' hours, then the rate of emptying the tank is $1/y$.
If there are 'n' pipes filling or emptying a tank, the time taken to fill or empty the tank will be $(1/a + 1/b + 1/c + .........+ 1/n)$ hours.
If a pipe can fill a tank in 'x' hours, then the time taken by the pipe to fill half the tank is $x/2$ hours.
If two pipes A and B can fill a tank in 'x' hours and 'y' hours respectively, then the time taken by both pipes working together to fill the tank is given by the formula: $(xy)/(x+y)$ hours.
If two pipes A and B can fill a tank in 'x' hours and 'y' hours respectively, then the time taken by both pipes working alternatively to fill the tank is given by the formula:$ (2xy)/(x+y) $hours.
If a pipe can fill a tank in 'x' hours, and it is kept open for 't' hours, then the fraction of the tank filled is given by the formula: $t/x$.
If a pipe can empty a tank in 'x' hours, and it is kept open for 't' hours, then the fraction of the tank emptied is given by the formula: t/x.
If a pipe can fill a tank in 'x' hours and empty the same tank in 'y' hours, then the net filling time is given by the formula: $(xy)/(y-x)$ hours.
If a pipe can fill a tank in 'x' hours and the same pipe can empty the tank in 'y' hours, then the net filling time is given by the formula: $(xy)/(x-y)$ hours.
If the capacity of the tank is 'C' and the rate of filling or emptying the tank is 'R', then the time taken to fill or empty the tank is given by the formula: $C/R$.

These formulas, shortcuts, rules, tricks, and tips can help you solve Pipes and Cisterns problems quickly and accurately. However, practice and understanding the underlying concepts are essential for mastering this topic.