Abhi is twice as old as his daughter. Five years ago, his age was four times his daughter's age. If the present age of the daugheter is x yr. then

Options

A. `2 (x-5) = 4 (2x - 5)`
B. `2 (x -5) = 4 (2 x +5)`
C. `4 (x -5) = 2x - 5`
D. `4 (x +5) = 2 (2x - 5)`

Answer

To solve the problem, we will set up equations based on the information given in the question.

### Step-by-Step Solution:

1. **Define Variables:**
- Let the present age of Abhi's daughter be \( x \) years.
- Since Abhi is twice as old as his daughter, Abhi's present age will be \( 2x \) years.

2. **Determine Ages 5 Years Ago:**
- Five years ago, the daughter's age was \( x - 5 \) years.
- Five years ago, Abhi's age was \( 2x - 5 \) years.

3. **Set Up the Equation:**
- According to the problem, five years ago, Abhi's age was four times his daughter's age. This can be expressed as:
\[ 2x - 5 = 4(x - 5) \]

4. **Expand and Simplify the Equation:**
- Expanding the right side:
\[ 2x - 5 = 4x - 20 \]
- Now, rearranging the equation to isolate \( x \):
\[ 2x - 4x = -20 + 5 \]
\[ -2x = -15 \]
\[ 2x = 15 \]
\[ x = \frac{15}{2} = 7.5 \]

5. **Conclusion:**
- The present age of Abhi's daughter is \( 7.5 \) years, and Abhi's present age is \( 2 \times 7.5 = 15 \) years.