Solve the following word problem.
Two empty storage reservoirs, X and Y, are filled with water. If an identical volume of water is pumped into both reservoirs, reservoir X becomes $\frac{3}{\mathrm{8 }}$ full and reservoir Y becomes $\frac{2}{5}$ full. The total capacity of reservoir Y is what percent of the total capacity of reservoir X?

The correct option is 93.75%.

To find what percent the total capacity of reservoir Y is compared to the total capacity of reservoir X, let us analyze the given information step-by-step.

Let $C_X$ be the total capacity of reservoir X, and let $C_Y$ be the total capacity of reservoir Y.

An identical volume of water, let us call it $V$, is pumped into both empty reservoirs.

According to the problem statement:
Reservoir X becomes $\frac{3}{8}$ full.
Therefore, the volume of water pumped into reservoir X is:
$V=\frac{3}{8}{C}_X$

Reservoir Y becomes $\frac{2}{5}$ full.
Therefore, the volume of water pumped into reservoir Y is:
$V=\frac{2}{5}{C}_Y$

Since the same volume $V$ of water was pumped into both reservoirs, we can equate the two expressions for $V$:

$\frac{3}{8}{C}_X=\frac{2}{5}{C}_Y$

Now, let us find the ratio of the capacity of reservoir Y to the capacity of reservoir X ($\frac{C_Y}{C_X}$):

$\frac{C_Y}{C_X}=\frac{3}{8}\times \frac{5}{2}$

$\frac{C_Y}{C_X}=\frac{15}{16}$

To convert this ratio into a percentage, multiply by 100:

$\text{Percentage}=\left(\frac{15}{16}\right)\times 100\text{\%}$

$\text{Percentage}=\frac{1500}{16}\text{\%}=93.75\text{\%}$

Thus, the total capacity of reservoir Y is 93.75% of the total capacity of reservoir X.