Ashu's mother was three times as old as Ashu 5 years ago. After 5 years she will be twice as old as Ashu. How old is Ashu today?

Options

A. (a) 35 years
B. (b) 10 years
C. (c) 20 years
D. (d) 15 years

Explanation

To solve the problem step by step, let's define the variables and set up the equations based on the information given in the question.

### Step 1: Define the variables
Let:
- \( x \) = Age of Ashu's mother today
- \( y \) = Age of Ashu today

### Step 2: Set up the equations based on the information given
1. **Five years ago**:
- Ashu's mother was \( x - 5 \)
- Ashu was \( y - 5 \)
- According to the problem, Ashu's mother was three times as old as Ashu five years ago:
\[ x - 5 = 3(y - 5) \]
- Simplifying this equation:
\[ x - 5 = 3y - 15 \]
\[ x - 3y = -10 \quad \text{(Equation 1)} \]

2. **Five years from now**:
- Ashu's mother will be \( x + 5 \)
- Ashu will be \( y + 5 \)
- According to the problem, Ashu's mother will be twice as old as Ashu after five years:
\[ x + 5 = 2(y + 5) \]
- Simplifying this equation:
\[ x + 5 = 2y + 10 \]
\[ x - 2y = 5 \quad \text{(Equation 2)} \]

### Step 3: Solve the equations
Now we have a system of two equations:
1. \( x - 3y = -10 \) (Equation 1)
2. \( x - 2y = 5 \) (Equation 2)

We can solve these equations by elimination or substitution. Let's subtract Equation 1 from Equation 2:

\[ (x - 2y) - (x - 3y) = 5 - (-10) \]
This simplifies to:
\[ y = 15 \]

### Step 4: Substitute \( y \) back to find \( x \)
Now that we have \( y = 15 \), we can substitute it back into one of the original equations to find \( x \). Let's use Equation 2:

\[ x - 2(15) = 5 \]
\[ x - 30 = 5 \]
\[ x = 35 \]

### Conclusion
- Ashu's age today \( y = 15 \)
- Ashu's mother's age today \( x = 35 \)

### Final Answer
Ashu is **15 years old** today.

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