At present Satish is four Madhur's age. After eight years Satish will be 2.5 times Madhur's age then. "How many times will Satish'a age be in another eight years time with respect to Madhur's age then ?

Options

A. 5
B. 3
C. 2
D. 1.5

Answer

To solve the problem step by step, we will define the ages of Satish and Madhur and use the information provided in the question to find the required relationship between their ages after a certain period.

### Step-by-Step Solution:

1. **Define the Variables:**
Let Madhur's current age be \( x \).
Then, Satish's current age will be \( 4x \) (since Satish is four times Madhur's age).

2. **Calculate Ages After 8 Years:**
After 8 years:
- Madhur's age will be \( x + 8 \).
- Satish's age will be \( 4x + 8 \).

3. **Set Up the Equation:**
According to the problem, after 8 years, Satish's age will be 2.5 times Madhur's age:
\[ 4x + 8 = 2.5(x + 8) \]

4. **Expand and Simplify the Equation:**
Expanding the right side:
\[ 4x + 8 = 2.5x + 20 \]
Now, rearranging the equation:
\[ 4x - 2.5x = 20 - 8 \]
This simplifies to:
\[ 1.5x = 12 \]

5. **Solve for \( x \):**
Dividing both sides by 1.5:
\[ x = \frac{12}{1.5} = 8 \]
So, Madhur's current age is \( 8 \) years.

6. **Find Satish's Current Age:**
Since Satish's age is \( 4x \):
\[ 4x = 4 \times 8 = 32 \]
Thus, Satish's current age is \( 32 \) years.

7. **Calculate Ages After 16 Years:**
After another 8 years (which makes it a total of 16 years from now):
- Madhur's age will be \( 8 + 16 = 24 \) years.
- Satish's age will be \( 32 + 16 = 48 \) years.

8. **Determine the Ratio of Their Ages:**
Now, we need to find how many times Satish's age will be compared to Madhur's age:
\[ \text{Ratio} = \frac{\text{Satish's age}}{\text{Madhur's age}} = \frac{48}{24} = 2 \]

### Final Answer:
Satish's age will be **2 times** Madhur's age after another 8 years.

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