Question

The ratio of the present age of A and B is 4:7, and 6 years back the ratio was 2:5. What will be the ratio of their ages after 9 years?

• A. 5:7
• B. 5:9
• C. 7:10
• D. 6:11

Hint:

When solving age-related ratio problems, set up equations based on the given ratios, and solve for the unknown constant to find their present ages. Then calculate future ages by adding or subtracting as necessary.

Answer 1

The Correct Option is C

Let the present age of A be \( 4x \) and the present age of B be \( 7x \), where \( x \) is a constant. Step 1: Using the given condition 6 years ago.
The ratio of their ages 6 years ago was 2:5. Therefore, the equation for their ages 6 years ago is: \[ \frac{4x - 6}{7x - 6} = \frac{2}{5} \] Cross-multiply to solve for \( x \): \[ 5(4x - 6) = 2(7x - 6) \] Simplify: \[ 20x - 30 = 14x - 12 \] \[ 20x - 14x = 30 - 12 \] \[ 6x = 18 \] \[ x = 3 \] Step 2: Calculate the present ages of A and B.
Now that we know \( x = 3 \), the present age of A is: \[ 4x = 4 \times 3 = 12 \text{ years} \] The present age of B is: \[ 7x = 7 \times 3 = 21 \text{ years} \] Step 3: Find their ages after 9 years.
After 9 years, the age of A will be: \[ 12 + 9 = 21 \text{ years} \] The age of B will be: \[ 21 + 9 = 30 \text{ years} \] Step 4: Calculate the new ratio of their ages.
The new ratio of their ages after 9 years is: \[ \frac{21}{30} = \frac{7}{10} \] Step 5: Conclusion.
Therefore, the ratio of their ages after 9 years will be \( 7:10 \), which corresponds to option (3).