Raju got married 8years ago. His present age is 6/5 times his age at the time of his marriage Raju's sister was 10years younger to him at the time of his marriage. The present age of Raju's sister is ?

Options

A. a. 40
B. b. 38
C. c. 42
D. d. 44

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define Variables
Let Raju's age at the time of his marriage be \( x \) years.

### Step 2: Express Present Age
Since Raju got married 8 years ago, his present age is:
\[ \text{Present Age} = x + 8 \]

### Step 3: Set Up the Equation
According to the problem, Raju's present age is \( \frac{6}{5} \) times his age at the time of his marriage. Therefore, we can set up the equation:
\[ x + 8 = \frac{6}{5}x \]

### Step 4: Solve for \( x \)
To eliminate the fraction, multiply the entire equation by 5:
\[ 5(x + 8) = 6x \]
This simplifies to:
\[ 5x + 40 = 6x \]
Now, rearranging gives:
\[ 40 = 6x - 5x \]
\[ 40 = x \]

### Step 5: Find Raju's Present Age
Now that we have Raju's age at the time of marriage, we can find his present age:
\[ \text{Present Age} = x + 8 = 40 + 8 = 48 \text{ years} \]

### Step 6: Find Raju's Sister's Age at Marriage
Raju's sister was 10 years younger than him at the time of his marriage:
\[ \text{Sister's Age at Marriage} = x - 10 = 40 - 10 = 30 \text{ years} \]

### Step 7: Find Raju's Sister's Present Age
Since Raju's sister was 30 years old when Raju got married 8 years ago, her present age is:
\[ \text{Sister's Present Age} = 30 + 8 = 38 \text{ years} \]

### Conclusion
Thus, the present age of Raju's sister is **38 years**.

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