Six years ago, the respective ratio between the ages of Sia and her father that time was 1 : 7. The difference between the age of Sia’s father and Sia is 36 years. What will be Sia’s age 7 years from now ?

Options

A. 13years
B. 15 years
C. 21 years
D. 17 years

Answer

To solve the problem step by step, we will denote Sia's current age as \( S \) and her father's current age as \( F \).

### Step 1: Establish the ratio of their ages 6 years ago
Six years ago, the ratio of Sia's age to her father's age was given as 1:7. Therefore, we can express this as:
\[ \frac{S - 6}{F - 6} = \frac{1}{7} \]
This implies:
\[ 7(S - 6) = 1(F - 6) \]
Expanding this gives:
\[ 7S - 42 = F - 6 \]
Rearranging it, we have:
\[ F = 7S - 36 \quad \text{(Equation 1)} \]

### Step 2: Use the age difference
We are also given that the difference between Sia's father's age and Sia's age is 36 years:
\[ F - S = 36 \quad \text{(Equation 2)} \]

### Step 3: Substitute Equation 1 into Equation 2
Now, we can substitute Equation 1 into Equation 2:
\[ (7S - 36) - S = 36 \]
Simplifying this gives:
\[ 6S - 36 = 36 \]
Adding 36 to both sides:
\[ 6S = 72 \]
Dividing by 6:
\[ S = 12 \]

### Step 4: Find Sia's age 7 years from now
Now that we have Sia's current age, we can find her age 7 years from now:
\[ \text{Sia's age in 7 years} = S + 7 = 12 + 7 = 19 \]

### Conclusion
Thus, Sia will be 19 years old 7 years from now.