The ratio between the present ages of Omkar and Ram Krishan is 4:5 seven years ago, the ratio of their ages was 3:4. What is the present age of Ram Krishan?

Options

A. 28 years
B. 35 years
C. 21 years
D. Data inadequate

Answer

To find the present age of Ram Krishan, we will follow these steps:

1. **Define Variables**:
Let the present age of Omkar be \( X \) and the present age of Ram Krishan be \( Y \).

2. **Set Up the First Equation**:
According to the problem, the ratio of their present ages is given as \( 4:5 \). This can be expressed as:
\[ \frac{X}{Y} = \frac{4}{5} \]
From this, we can express \( X \) in terms of \( Y \):
\[ X = \frac{4}{5}Y \quad \text{(Equation 1)} \]

3. **Set Up the Second Equation**:
The problem also states that seven years ago, the ratio of their ages was \( 3:4 \). Seven years ago, Omkar's age would be \( X - 7 \) and Ram Krishan's age would be \( Y - 7 \). Thus, we can write:
\[ \frac{X - 7}{Y - 7} = \frac{3}{4} \]
Cross-multiplying gives us:
\[ 4(X - 7) = 3(Y - 7) \]
Expanding this, we have:
\[ 4X - 28 = 3Y - 21 \]
Rearranging gives us:
\[ 4X - 3Y = 7 \quad \text{(Equation 2)} \]

4. **Substituting Equation 1 into Equation 2**:
Now we substitute \( X \) from Equation 1 into Equation 2:
\[ 4\left(\frac{4}{5}Y\right) - 3Y = 7 \]
This simplifies to:
\[ \frac{16}{5}Y - 3Y = 7 \]
To combine the terms, we convert \( 3Y \) to a fraction with a denominator of 5:
\[ \frac{16}{5}Y - \frac{15}{5}Y = 7 \]
This simplifies to:
\[ \frac{1}{5}Y = 7 \]

5. **Solving for \( Y \)**:
Multiply both sides by 5 to solve for \( Y \):
\[ Y = 35 \]

6. **Conclusion**:
The present age of Ram Krishan is \( 35 \) years.