A man is `10` times older than his grandson. He is also `54` years older than him. Find the present age of the man.

Options

A. 60 years
B. 65 years
C. 70 years
D. 80 years

Answer

To solve the problem step by step, we will use algebraic equations based on the information given in the question.

### Step 1: Define Variables
Let the present age of the grandson be \( x \) years.

### Step 2: Express the Man's Age
According to the problem, the man is 10 times older than his grandson. Therefore, the man's age can be expressed as:
\[ \text{Man's age} = 10x \]

### Step 3: Set Up the Equation
The problem also states that the man is 54 years older than his grandson. We can set up the equation:
\[ 10x = x + 54 \]

### Step 4: Solve the Equation
Now, we will solve for \( x \):
1. Subtract \( x \) from both sides:
\[ 10x - x = 54 \]
\[ 9x = 54 \]

2. Divide both sides by 9:
\[ x = \frac{54}{9} \]
\[ x = 6 \]

### Step 5: Find the Man's Present Age
Now that we have the grandson's age, we can find the man's age:
\[ \text{Man's age} = 10x = 10 \times 6 = 60 \]

### Conclusion
The present age of the man is \( 60 \) years.

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