Mr Gupta is 4 times as old as his son. After 6 years, he will be 24 years older than his son. Find the present age of Mr Gupta

Options

A. 17 years
B. 20 years
C. 32 years
D. 25 years

Answer

To find the present age of Mr. Gupta, we can set up the problem using algebra. Let's break it down step by step.

### Step 1: Define the variables
Let the present age of Mr. Gupta's son be \( x \) years. Since Mr. Gupta is 4 times as old as his son, his present age will be \( 4x \) years.

### Step 2: Set up the equation for future ages
According to the problem, after 6 years, Mr. Gupta will be 24 years older than his son. After 6 years, the son's age will be \( x + 6 \) and Mr. Gupta's age will be \( 4x + 6 \).

### Step 3: Write the equation based on the future ages
We can set up the equation based on the information given:
\[ 4x + 6 = (x + 6) + 24 \]

### Step 4: Simplify the equation
Now, simplify the right side of the equation:
\[ 4x + 6 = x + 30 \]

### Step 5: Rearrange the equation
To solve for \( x \), we need to get all terms involving \( x \) on one side:
\[ 4x - x = 30 - 6 \]
\[ 3x = 24 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 3:
\[ x = \frac{24}{3} = 8 \]

### Step 7: Find Mr. Gupta's present age
Now that we have the son's age, we can find Mr. Gupta's age:
\[ \text{Mr. Gupta's age} = 4x = 4 \times 8 = 32 \]

### Final Answer
The present age of Mr. Gupta is **32 years**.

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