Mukesh invests Rs. $2Z$ at simple interest at a rate of 20\% per annum for $X$ years and earns simple interest of Rs. $Z$. Sonu invests Rs. $3Z$ at simple interest at a rate of $Y\%$ per annum for $X$ years and earns simple interest of Rs. $2Z$. What is $X$ as a percentage of $Y$?

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**Solution:**

1. For Mukesh, simple interest (SI) is given by:
   $$SI = \frac{P 	imes R 	imes T}{100}$$
   Here, $P = 2Z$, $R = 20\%$, $T = X$ years, and $SI = Z$.

2. Substitute the values:
   $$Z = \frac{2Z 	imes 20 	imes X}{100}$$

3. Simplify the equation:
   $$Z = \frac{40ZX}{100} = \frac{2ZX}{5}$$

4. Divide both sides by $Z$ (assuming $Z 
eq 0$):
   $$1 = \frac{2X}{5} \implies X = \frac{5}{2} = 2.5$$

5. For Sonu, simple interest is:
   $$SI = \frac{P 	imes R 	imes T}{100}$$
   Here, $P = 3Z$, $R = Y\%$, $T = X = 2.5$ years, and $SI = 2Z$.

6. Substitute the values:
   $$2Z = \frac{3Z 	imes Y 	imes 2.5}{100}$$

7. Simplify:
   $$2Z = \frac{7.5ZY}{100}$$

8. Divide both sides by $Z$:
   $$2 = \frac{7.5Y}{100} \implies 2 = 0.075Y$$

9. Solve for $Y$:
   $$Y = \frac{2}{0.075} = \frac{200}{7.5} = 26.6667$$

10. Now, find $X$ as a percentage of $Y$:
    $$\frac{X}{Y} 	imes 100 = \frac{2.5}{26.6667} 	imes 100 = 9.375\%$$

**Answer:** $9.375\%$

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