There are two empty vessels, P and Q. When an equal quantity of juice is poured into both vessels, vessel P becomes $ $\frac{3}{8}$ $ full, and vessel Q becomes $ $\frac{2}{5}$ $ full. What is the capacity of vessel Q as a percentage of the capacity of vessel P?

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**Solution:**

1. Let the equal quantity of juice poured into both vessels be $ x $.

2. For vessel P, $$ x = \frac{3}{8} \times \text{Capacity of P}$ $.
   Therefore, $$ \text{Capacity of P} = \frac{8}{3} x $$.

3. For vessel Q, $$ x = \frac{2}{5} \times \text{Capacity of Q}$ $.
   Therefore, $$ \text{Capacity of Q} = \frac{5}{2} x $$.

4. To find the capacity of Q as a percentage of capacity of P:

$$
   $\frac{\text{Capacity of Q}}{\text{Capacity of P}} \times 100 = \frac{\frac{5}{2} x}{\frac{8}{3} x} \times 100 = \frac{5}{2} \times \frac{3}{8} \times 100$
   $$

5. Simplify the expression:

$$
   $= \frac{5 \times 3}{2 \times 8} \times 100 = \frac{15}{16} \times 100 = 93.75\%$
   $$

**Answer:** 93.75\%

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