Mohit is 20 years younger than his father. Three years ago, Mohit's age was one-sixth the age of his father, then find the present age of Mohit.

Options

A. 7 years
B. 6 years
C. 8 years
D. 4 years

Answer

To find Mohit's present age, we can follow these steps:

### Step 1: Define Variables
Let the present age of Mohit's father be \( x \) years. Since Mohit is 20 years younger than his father, we can express Mohit's age as:
\[ \text{Mohit's age} = x - 20 \]

### Step 2: Set Up the Equation for Ages Three Years Ago
Three years ago, Mohit's age would be:
\[ \text{Mohit's age 3 years ago} = (x - 20) - 3 = x - 23 \]
Similarly, three years ago, his father's age would be:
\[ \text{Father's age 3 years ago} = x - 3 \]

### Step 3: Use the Given Condition
According to the problem, three years ago, Mohit's age was one-sixth of his father's age:
\[ x - 23 = \frac{1}{6}(x - 3) \]

### Step 4: Clear the Fraction
To eliminate the fraction, multiply both sides of the equation by 6:
\[ 6(x - 23) = x - 3 \]
This simplifies to:
\[ 6x - 138 = x - 3 \]

### Step 5: Rearrange the Equation
Now, let's rearrange the equation to isolate \( x \):
\[ 6x - x = 138 - 3 \]
This simplifies to:
\[ 5x = 135 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 5:
\[ x = \frac{135}{5} = 27 \]

### Step 7: Find Mohit's Present Age
Now that we have the present age of Mohit's father, we can find Mohit's age:
\[ \text{Mohit's age} = x - 20 = 27 - 20 = 7 \]

### Conclusion
Thus, the present age of Mohit is:
\[ \boxed{7} \text{ years} \]

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