The ratio of the ages of two sisters today is 1 : 2. However, after 4 years, the ratio would be 2:3. What is the age of the eldest sister today?
A. 12 years B. 8 years C. 6 years D. 10 years
Correct Answer: B
Explanation
To find the age of the eldest sister, follow these steps:
1. Set Up the Initial Ratio: - Let the current ages of the two sisters be \( x \) and \( 2x \) respectively, where \( x \) is the age of the younger sister and \( 2x \) is the age of the eldest sister.
2. Use the Future Ratio: - After 4 years, the ages of the sisters will be \( x + 4 \) and \( 2x + 4 \). - The new ratio of their ages will be 2:3: \[ \frac{x + 4}{2x + 4} = \frac{2}{3} \]
3. Solve the Ratio Equation: - Cross-multiply to solve for \( x \): \[ 3(x + 4) = 2(2x + 4) \] \[ 3x + 12 = 4x + 8 \] \[ 12 - 8 = 4x - 3x \] \[ 4 = x \]
4. Find the Eldest Sister's Age: - The age of the eldest sister is \( 2x \): \[ 2x = 2 \times 4 = 8 \]