The ratio of present ages of Simi and Seema is `5 : 4`. After 9 years the ratio of their ages will be `8 : 7`. What is Simi's present age (in years)?

Options

A. 12
B. 15
C. 24
D. 21

Answer

To solve the problem, we need to find Simi's present age based on the given ratios of her age compared to Seema's age. Let's break it down step by step.

### Step 1: Define the present ages
Let the present age of Simi be \(5x\) and the present age of Seema be \(4x\), based on the ratio \(5:4\).

### Step 2: Set up the equation for ages after 9 years
After 9 years, Simi's age will be \(5x + 9\) and Seema's age will be \(4x + 9\). According to the problem, the ratio of their ages after 9 years will be \(8:7\).

### Step 3: Write the equation based on the new ratio
We can set up the equation:
\[ \frac{5x + 9}{4x + 9} = \frac{8}{7} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 7(5x + 9) = 8(4x + 9) \]

### Step 5: Expand both sides
Expanding both sides results in:
\[ 35x + 63 = 32x + 72 \]

### Step 6: Rearrange the equation
Now, we will rearrange the equation to isolate \(x\):
\[ 35x - 32x = 72 - 63 \]
This simplifies to:
\[ 3x = 9 \]

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

### Step 8: Find Simi's present age
Now, substituting \(x\) back into the expression for Simi's age:
\[ \text{Simi's age} = 5x = 5 \times 3 = 15 \]

### Conclusion
Simi's present age is **15 years**.

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