The ratio of present ages of R and S is 5 : 7, 5 years ago R was 30 years old. What was the age (in years) of S 10 years ago?

Options

A. 39
B. 32
C. 49
D. 42

Answer

To solve the problem step by step, we will follow the information given in the question:

### Step 1: Define the present ages of R and S
Given the ratio of the present ages of R and S is 5:7, we can express their ages in terms of a variable \( x \):
- Present age of R = \( 5x \)
- Present age of S = \( 7x \)

**Hint:** Use a variable to represent the ratio of ages to simplify calculations.

### Step 2: Use the information about R's age 5 years ago
We know that 5 years ago, R was 30 years old. Therefore, we can set up the equation:
\[ 5x - 5 = 30 \]

**Hint:** Remember to adjust the present age by subtracting the number of years ago to find the past age.

### Step 3: Solve for \( x \)
Now, we will solve the equation:
\[ 5x - 5 = 30 \]
Adding 5 to both sides:
\[ 5x = 35 \]
Now, divide by 5:
\[ x = 7 \]

**Hint:** Isolate the variable by performing inverse operations to find its value.

### Step 4: Find the present age of S
Now that we have \( x \), we can find the present age of S:
\[ \text{Present age of S} = 7x = 7 \times 7 = 49 \text{ years} \]

**Hint:** Substitute the value of \( x \) back into the expression for S's age.

### Step 5: Calculate S's age 10 years ago
To find S's age 10 years ago, we subtract 10 from the present age of S:
\[ \text{Age of S 10 years ago} = 49 - 10 = 39 \text{ years} \]

**Hint:** Remember to subtract the number of years from the present age to find the past age.

### Conclusion
Thus, the age of S 10 years ago was **39 years**.

**Final Answer:** 39 years