The ratio of the ages of a father to that of his son is 5 : 2 If the product of their ages (in years) is 1000, then find the father's age after 10 yr from now

Options

A. 50 yr
B. 60 yr
C. 80 yr
D. 100 yr

Answer

To solve the problem step by step, we will follow the given information about the ratio of the ages and the product of their ages.

### Step 1: Understand the ratio of ages
The ratio of the ages of the father to the son is given as 5:2. This means that if we let the father's age be represented as \(5x\) and the son's age as \(2x\), where \(x\) is a common multiplier.

### Step 2: Set up the equation for the product of their ages
According to the problem, the product of their ages is 1000. Therefore, we can write the equation:
\[ (5x) \times (2x) = 1000 \]

### Step 3: Simplify the equation
This simplifies to:
\[ 10x^2 = 1000 \]

### Step 4: Solve for \(x^2\)
To isolate \(x^2\), divide both sides of the equation by 10:
\[ x^2 = \frac{1000}{10} = 100 \]

### Step 5: Solve for \(x\)
Now, take the square root of both sides to find \(x\):
\[ x = \sqrt{100} = 10 \]

### Step 6: Find the father's age
Now that we have the value of \(x\), we can find the father's age:
\[ \text{Father's age} = 5x = 5 \times 10 = 50 \text{ years} \]

### Step 7: Calculate the father's age after 10 years
To find the father's age after 10 years, we simply add 10 to the current age:
\[ \text{Father's age after 10 years} = 50 + 10 = 60 \text{ years} \]

### Final Answer
The father's age after 10 years will be **60 years**.

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