The ratio of the present ages of Rupa and her daughter is ` 7 : 3`. When Rupa was 26 years old, her daughter was 6 years old . Find the present age of Rupa. (in years)

Answer

To solve the problem step by step, we will denote Rupa's present age as \( x \) and her daughter's present age as \( y \).

### Step 1: Set up the ratio equation
According to the problem, the ratio of Rupa's present age to her daughter's present age is \( 7:3 \). This can be expressed as:
\[ \frac{x}{y} = \frac{7}{3} \]
Cross-multiplying gives us:
\[ 3x = 7y \]
This is our **Equation 1**.

### Step 2: Set up the age difference equation
We know that when Rupa was 26 years old, her daughter was 6 years old. The difference in their ages is:
\[ 26 - 6 = 20 \text{ years} \]
This age difference remains constant. Therefore, we can express this as:
\[ x - y = 20 \]
This is our **Equation 2**.

### Step 3: Solve the equations
We now have two equations:
1. \( 3x - 7y = 0 \) (Equation 1)
2. \( x - y = 20 \) (Equation 2)

We can express \( y \) from Equation 2:
\[ y = x - 20 \]

### Step 4: Substitute \( y \) in Equation 1
Substituting \( y \) in Equation 1:
\[ 3x - 7(x - 20) = 0 \]
Expanding this gives:
\[ 3x - 7x + 140 = 0 \]
Combining like terms:
\[ -4x + 140 = 0 \]
Solving for \( x \):
\[ 4x = 140 \\ x = \frac{140}{4} = 35 \]

### Step 5: Find \( y \)
Now substituting \( x = 35 \) back into Equation 2 to find \( y \):
\[ y = 35 - 20 = 15 \]

### Conclusion
Thus, the present age of Rupa is \( \boxed{35} \) years.

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