7 years ago, the ratio of the ages of Anirudh to that of Bhavana, was 7:9. Chandhu is 12 years older than Anirudh and 12 years younger than Bhavana. What is Chandhu's present age?

Options

A. A) 91 years
B. B) 115 years
C. C) 103 years
D. D) Can't be determined

Answer

To solve the problem step by step, we will denote the ages of Anirudh and Bhavana 7 years ago and then find Chandhu's present age.

### Step 1: Define Variables
Let Anirudh's age 7 years ago be \( 7x \) and Bhavana's age 7 years ago be \( 9x \), where \( x \) is a common multiplier.

### Step 2: Set Up the Age Equations
Since we know their ages 7 years ago, we can express their current ages as:
- Anirudh's current age = \( 7x + 7 \)
- Bhavana's current age = \( 9x + 7 \)

### Step 3: Use the Information About Chandhu
We know that Chandhu is 12 years older than Anirudh and 12 years younger than Bhavana. Therefore, we can express Chandhu's age in two ways:
1. \( \text{Chandhu's age} = (7x + 7) + 12 = 7x + 19 \)
2. \( \text{Chandhu's age} = (9x + 7) - 12 = 9x - 5 \)

### Step 4: Set the Two Expressions for Chandhu's Age Equal
Since both expressions represent Chandhu's age, we can set them equal to each other:
\[ 7x + 19 = 9x - 5 \]

### Step 5: Solve for \( x \)
To solve for \( x \), we will rearrange the equation:
\[ 19 + 5 = 9x - 7x \]
\[ 24 = 2x \]
\[ x = 12 \]

### Step 6: Find Anirudh's Current Age
Now that we have \( x \), we can find Anirudh's current age:
\[ \text{Anirudh's current age} = 7x + 7 = 7(12) + 7 = 84 + 7 = 91 \]

### Step 7: Find Bhavana's Current Age
Next, we find Bhavana's current age:
\[ \text{Bhavana's current age} = 9x + 7 = 9(12) + 7 = 108 + 7 = 115 \]

### Step 8: Find Chandhu's Current Age
Finally, we can find Chandhu's current age using either expression:
\[ \text{Chandhu's age} = 7x + 19 = 7(12) + 19 = 84 + 19 = 103 \]

Thus, Chandhu's present age is **103 years**.