The ages of A and B are in the ratio 4:7, respectively. After 8 years, the ratio of their ages will be 2:3. What is the sum of the present ages of A and B (in years)?
- A44
- B36
- C38
- D42
Solution & Step-by-step Explanation
Let the present age of A be 4x and B be 7x.
After 8 years:
Age of A=4x+8
Age of B=7x+8
Given that the ratio becomes 2:3:
7x+8
4x+8
=
3
2
Cross-multiplying:
3(4x+8)=2(7x+8)
12x+24=14x+16
24−16=14x−12x
8=2x⟹x=4
The present ages are:
Age of A=4×4=16 years
Age of B=7×4=28 years
Sum of their present ages:
Sum=16+28=42 years
After 8 years:
Age of A=4x+8
Age of B=7x+8
Given that the ratio becomes 2:3:
7x+8
4x+8
=
3
2
Cross-multiplying:
3(4x+8)=2(7x+8)
12x+24=14x+16
24−16=14x−12x
8=2x⟹x=4
The present ages are:
Age of A=4×4=16 years
Age of B=7×4=28 years
Sum of their present ages:
Sum=16+28=42 years