Two numbers are in the ratio $2 : 3$. Their sum is $135$. Find the numbers.

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**Solution:**

1. Let the two numbers be $2x$ and $3x$ since their ratio is $2 : 3$.

2. Their sum is given as:
   $$2x + 3x = 135$$
   $$5x = 135$$

3. Solve for $x$:
   $$x = \frac{135}{5} = 27$$

4. Find the two numbers:
   - First number: $2x = 2 	imes 27 = 54$
   - Second number: $3x = 3 	imes 27 = 81$

**Answer:** $54, 81$

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