The ratio between present age of Kunal and Ganesh is 3 : 5. If 4 years hence Kunal will be younger than Ganesh by 12 years. What is the present age of Kunal ?

Options

A. 17 years
B. 19 years
C. 22 years
D. None of these

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Define the variables based on the given ratio
Let the present age of Kunal be represented as \(3x\) and the present age of Ganesh be represented as \(5x\), based on the ratio of their ages which is 3:5.

**Hint:** Use the ratio provided in the question to express the ages in terms of a variable.

### Step 2: Set up the equation for their ages 4 years hence
In 4 years, Kunal's age will be \(3x + 4\) and Ganesh's age will be \(5x + 4\). According to the problem, Kunal will be younger than Ganesh by 12 years at that time.

**Hint:** Remember to add 4 years to both ages to account for the future ages.

### Step 3: Write the equation based on the age difference
From the problem statement, we can set up the equation:
\[ (5x + 4) - (3x + 4) = 12 \]
This simplifies to:
\[ 5x + 4 - 3x - 4 = 12 \]

**Hint:** Rearranging the equation correctly will help isolate the variable.

### Step 4: Simplify the equation
Simplifying the left side gives:
\[ 2x = 12 \]

**Hint:** Combine like terms to simplify the equation.

### Step 5: Solve for \(x\)
Dividing both sides by 2 gives:
\[ x = 6 \]

**Hint:** To find the value of \(x\), perform the arithmetic operation needed to isolate \(x\).

### Step 6: Find Kunal's present age
Now that we have \(x\), we can find Kunal's present age:
\[ \text{Kunal's present age} = 3x = 3 \times 6 = 18 \]

**Hint:** Substitute the value of \(x\) back into the expression for Kunal's age.

### Conclusion
The present age of Kunal is **18 years**.

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