The ratio of ages of Krishna and Balram is 3:4. Four years earlier the ratio was 5:7. Find the present ages of Krshna and Balram:

Options

A. 15 years, 20 years
B. 24 years, 32 years
C. 16 years, 20 years
D. 32 years, 4 years

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Variables
Let the present age of Krishna be \( 3x \) and the present age of Balram be \( 4x \), based on the given ratio of their ages, which is \( 3:4 \).

### Step 2: Determine Their Ages Four Years Ago
Four years ago, Krishna's age would be \( 3x - 4 \) and Balram's age would be \( 4x - 4 \).

### Step 3: Set Up the Equation Based on the Given Ratio Four Years Ago
According to the problem, the ratio of their ages four years ago was \( 5:7 \). Therefore, we can set up the equation:
\[ \frac{3x - 4}{4x - 4} = \frac{5}{7} \]

### Step 4: Cross-Multiply to Eliminate the Fraction
Cross-multiplying gives us:
\[ 7(3x - 4) = 5(4x - 4) \]

### Step 5: Expand Both Sides
Expanding both sides results in:
\[ 21x - 28 = 20x - 20 \]

### Step 6: Rearrange the Equation
Now, we will rearrange the equation to isolate \( x \):
\[ 21x - 20x = -20 + 28 \]
\[ x = 8 \]

### Step 7: Calculate the Present Ages
Now that we have \( x \), we can find the present ages:
- Krishna's present age:
\[ 3x = 3 \times 8 = 24 \text{ years} \]
- Balram's present age:
\[ 4x = 4 \times 8 = 32 \text{ years} \]

### Final Answer
The present ages are:
- Krishna: 24 years
- Balram: 32 years

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