Ravi weighs `(2)/(3)` rd of the weight of his elder brother and `(5)/(9)`th of the weight of his father. Find the ratio of the weight of his elder brother to the weight of his father.

Answer

To find the ratio of the weight of Ravi's elder brother to the weight of his father, we can follow these steps:

### Step 1: Define Variables
Let the weight of Ravi's elder brother be \( x \) and the weight of Ravi's father be \( y \).

### Step 2: Set Up Equations
According to the problem:
- Ravi weighs \( \frac{2}{3} \) of the weight of his elder brother:
\[ \text{Weight of Ravi} = \frac{2}{3}x \]
- Ravi weighs \( \frac{5}{9} \) of the weight of his father:
\[ \text{Weight of Ravi} = \frac{5}{9}y \]

### Step 3: Equate the Two Expressions for Ravi's Weight
Since both expressions represent Ravi's weight, we can set them equal to each other:
\[ \frac{2}{3}x = \frac{5}{9}y \]

### Step 4: Cross-Multiply to Eliminate Fractions
Cross-multiplying gives us:
\[ 2 \cdot 9x = 5 \cdot 3y \]
This simplifies to:
\[ 18x = 15y \]

### Step 5: Rearrange to Find the Ratio
Now, we can rearrange this equation to find the ratio of \( x \) to \( y \):
\[ \frac{x}{y} = \frac{15}{18} \]

### Step 6: Simplify the Ratio
We can simplify \( \frac{15}{18} \) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3:
\[ \frac{x}{y} = \frac{5}{6} \]

### Step 7: State the Final Ratio
Thus, the ratio of the weight of Ravi's elder brother to the weight of his father is:
\[ \text{Ratio of elder brother to father} = 5:6 \]

---