Elena's age after 15 years will be 5 times her age 5 years back. What is the present age of Elena?

Options

A. 10 years
B. 37 years
C. 35 years
D. 11 years

Answer

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

### Step 1: Define the present age
Let Elena's present age be represented by \( X \).

### Step 2: Express her age after 15 years
After 15 years, Elena's age will be:
\[ X + 15 \]

### Step 3: Express her age 5 years back
Five years back, Elena's age was:
\[ X - 5 \]

### Step 4: Set up the equation based on the problem statement
According to the problem, Elena's age after 15 years will be 5 times her age 5 years back. Therefore, we can set up the equation:
\[ X + 15 = 5 \times (X - 5) \]

### Step 5: Simplify the equation
Now, we will simplify the equation:
\[ X + 15 = 5(X - 5) \]
\[ X + 15 = 5X - 25 \]

### Step 6: Rearrange the equation
Next, we will rearrange the equation to isolate \( X \):
\[ X + 15 + 25 = 5X \]
\[ X + 40 = 5X \]

### Step 7: Move all terms involving \( X \) to one side
Now, we will move \( X \) to the right side:
\[ 40 = 5X - X \]
\[ 40 = 4X \]

### Step 8: Solve for \( X \)
Now, we will solve for \( X \):
\[ X = \frac{40}{4} \]
\[ X = 10 \]

### Conclusion
Thus, Elena's present age is \( 10 \) years.