Rakhi's mother is four times as old as Rakhi. After `5` years, her mother will be three times as old as she will be then. Find their present ages.

Options

A. `40,20`
B. `50,15`
C. `40,10`
D. `45,10`

Answer

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

### Step 1: Define the Variables
Let Rakhi's current age be \( x \).
Then, Rakhi's mother's current age will be \( 4x \) (since she is four times as old as Rakhi).

### Step 2: Set Up the Equation for Future Ages
According to the problem, after 5 years:
- Rakhi's age will be \( x + 5 \).
- Her mother's age will be \( 4x + 5 \).

The problem states that after 5 years, Rakhi's mother will be three times as old as Rakhi. Therefore, we can set up the equation:
\[ 4x + 5 = 3(x + 5) \]

### Step 3: Expand the Equation
Now, we will expand the right side of the equation:
\[ 4x + 5 = 3x + 15 \]

### Step 4: Rearrange the Equation
Next, we will rearrange the equation to isolate \( x \):
\[ 4x + 5 - 3x = 15 \]
This simplifies to:
\[ x + 5 = 15 \]

### Step 5: Solve for \( x \)
Now, we will solve for \( x \):
\[ x = 15 - 5 \]
\[ x = 10 \]

### Step 6: Find Rakhi's Mother's Age
Now that we have Rakhi's age, we can find her mother's age:
\[ \text{Mother's age} = 4x = 4 \times 10 = 40 \]

### Conclusion
Rakhi's current age is \( 10 \) years, and her mother's current age is \( 40 \) years.

---