The product of Ramus age (in years) five years ago with his age (in years) 9 years later is 15. Find Ramus present age.

Answer

To solve the problem step by step, let's denote Ramu's present age as \( x \).

### Step 1: Set up the equation
Ramu's age 5 years ago would be \( x - 5 \) and his age 9 years later would be \( x + 9 \). According to the problem, the product of these two ages is equal to 15. Therefore, we can write the equation:
\[ (x - 5)(x + 9) = 15 \]

### Step 2: Expand the equation
Now, we will expand the left-hand side of the equation:
\[ x^2 + 9x - 5x - 45 = 15 \]
This simplifies to:
\[ x^2 + 4x - 45 = 15 \]

### Step 3: Rearrange the equation
Next, we will move 15 to the left side to set the equation to zero:
\[ x^2 + 4x - 45 - 15 = 0 \]
This simplifies to:
\[ x^2 + 4x - 60 = 0 \]

### Step 4: Factor the quadratic equation
Now, we will factor the quadratic equation. We need two numbers that multiply to -60 and add up to 4. The numbers 10 and -6 work:
\[ (x + 10)(x - 6) = 0 \]

### Step 5: Solve for \( x \)
Setting each factor equal to zero gives us:
1. \( x + 10 = 0 \) → \( x = -10 \)
2. \( x - 6 = 0 \) → \( x = 6 \)

### Step 6: Determine the valid solution
Since age cannot be negative, we discard \( x = -10 \). Therefore, Ramu's present age is:
\[ \boxed{6} \]