Arithmetic aptitude :: Pipes and Cisterns :: Data Sufficiency 2

• Pipes and Cisterns - Solved Examples
• Pipes and Cisterns - Data Sufficiency 1
• Pipes and Cisterns - Data Sufficiency 2
• Pipes and Cisterns - Important Formulas and Facts

1. Inlet:

An Inlet is a pipe which is connected with a tank or cistern or reservoir, which fills it.

2. Outlet:

 An Outlet is a pipe which is connected with a tank or cistern or reservoir, which empties it.

3. If an inlet can fill a tank in $x$ hours, then, part filled in $1$ hour $=\frac{1}{x}$.

4. If an outlet can empty a tank in $y$ hours, then: part emptied in $1$ hour $=\frac{1}{y}$.

5. If a pipe $A$ can fill a cistern in $x$ hours and another pipe $B$ can empty the full tank in $y$ hours (where $y>x$), then on opening both

the pipes, then, the net part filled in $1$ hour $=\left(\frac{1}{x}-\frac{1}{y}\right)$.

6. If an inlet can fill a reservoir in $x$ hours and another outlet can empty the full tank in $y$ hours (where $x>y$), then on opening both

inlet and outlet, then, the net part emptied in $1$ hour $=\left(\frac{1}{y}-\frac{1}{x}\right)$.

A tank is fitted with two taps $A$ and $B$. In how much time will the tank be full if both the taps are opened together ?

I. $A$ is $50\%$ more efficient than $B$.

II. $A$ alone takes $16$ hours to fill the tank.

III. $B$ alone takes $24$ hours to fill the tank.

Answer:

Explanation:

II. $A$’s $1$ hour work $=\frac{1}{16}$.

Suppose $B$ fills the tank in $x$ hours. Then, $B$’s $1$ hour work $=\frac{1}{x}$.

I. Work done by $A$ in $1$ hour $=150\%$ of $\frac{1}{x}$ $=\left(\frac{1}{x}\times\frac{150}{100}\right)$  $=\frac{3}{2x}$.

$\therefore\frac{3}{2x}=\frac{1}{16}$

$\Leftrightarrow x=24$.

So, $B$ can fill the tank in 24 hours.

$(A+B)$’s $1$ hour work $=\left(\frac{1}{16}+\frac{1}{24}\right)$ $=\frac{5}{48}$.

$\therefore $ $(A+B)$ can fill the tank in $\frac{48}{5}$ hrs.

Thus I & II give the answer.

III. Work done by $B$ in $1$ hour $=\frac{1}{24}$.

From II & III, we get the same answer.

From III & I, we get :

$A$’s $1$ hour work $=150\%$ of $\frac{1}{24}$ $=\left(\frac{1}{24}\times\frac{150}{100}\right)$ $=\frac{1}{16}$.

Thus, III & I, we get the answer.

$\therefore$  Correct answer is (E).

• Pipes and Cisterns - Solved Examples
• Pipes and Cisterns - Data Sufficiency 1
• Pipes and Cisterns - Data Sufficiency 2