Question

The graph above shows the amount of water remaining in a tank each time a pail was used to remove $x$ gallons of water. If $5$ gallons were in the tank originally and $2\frac{1}{2}$ gallons remained after the last pail containing $x$ gallons was removed, what is the value of $x$ ?

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

Answer: (B)

$\frac{1}{3}$

Given, amount of water removed each time a pile is used $=$ $x$

Initial amount of water in the tank $=$ $5$

Final amount of water in the tank $=$ $2\frac{1}{2}$

From the given graph, we can observe that:

when the $6^{th}$ pile is removed, volume of water left is $3$ gallons and the number of piles used till that point is ${}^{\prime }{6}^{\prime }$.

Hence, amount of water removed $=$ (Number of piles used) $\times$ (Amount of water removed each time a pile is used)

(Initial Amount - of water in the tank) $-$ (Amount of water left in the tank after $6$ piles are removed) $=$ $8$ $\times$ $x$

$\Rightarrow (5$ $-$ $3)$ $=$ $6x$

$\Rightarrow 2$ $=$ $6x$

$\Rightarrow x$ $=$ $\frac{1}{3}$

$\Rightarrow x$ $=$ $0.333$

Therefore, the value of ${}^{\prime }{x}^{\prime }$ is ${}^{\prime }{0.333}^{\prime }$.