2026 · Q20
The ratio of the present age of X to that of Y is 4:5. k (less than 10) years ago, this ratio was 1:2. How many values of k are possible if the ages are expressed in complete years?
Elementary MathematicsRatio and Proportion
- A1
- B2
- C3
- DMore than 3
Explanation
Write the present ages as 4t and 5t. Then (4t−k)/(5t−k)=1/2 gives 8t−2k=5t−k, i.e. k=3t. With k<10 and positive ages, t=1,2,3 yield k=3,6,9 — three possible values, option C.