At present, the ratio of the ages of Maya and Chhaya is 6:5 and fifteen years from now, the ratio will get changed to 9:8. Maya's present age is

Options

A. 21 years
B. 24 years
C. 30 years
D. 40 years

Answer

To find Maya's present age, we can follow these steps:

### Step 1: Set up the variables
Let the present age of Maya be \(6x\) and the present age of Chhaya be \(5x\), where \(x\) is a common multiplier.

### Step 2: Write the future ages
Fifteen years from now, Maya's age will be \(6x + 15\) and Chhaya's age will be \(5x + 15\).

### Step 3: Set up the ratio equation
According to the problem, the ratio of their ages after 15 years will be \(9:8\). Therefore, we can write the equation:
\[ \frac{6x + 15}{5x + 15} = \frac{9}{8} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 8(6x + 15) = 9(5x + 15) \]

### Step 5: Expand both sides
Expanding both sides of the equation:
\[ 48x + 120 = 45x + 135 \]

### Step 6: Rearrange the equation
Now, we will rearrange the equation to isolate \(x\):
\[ 48x - 45x = 135 - 120 \]
\[ 3x = 15 \]

### Step 7: Solve for \(x\)
Dividing both sides by 3 gives:
\[ x = 5 \]

### Step 8: Find Maya's present age
Now we can find Maya's present age:
\[ \text{Maya's present age} = 6x = 6 \times 5 = 30 \text{ years} \]

Thus, Maya's present age is **30 years**.

---