2019 · Q73
Radha and Rani are sisters. Five years back, the age of Radha was three times that of Rani, but one year back the age of Radha was two times that of Rani. What is the age difference between them?
Elementary MathematicsAlgebra
- A8
- B9
- C10
- D11
Explanation
Let Radha be R and Rani r. Five years back: R − 5 = 3(r − 5); one year back: R − 1 = 2(r − 1), so R = 2r − 1. Substituting: (2r − 1) − 5 = 3r − 15, i.e. 2r − 6 = 3r − 15, giving r = 9 and R = 17. The age difference is 17 − 9 = 8 years. The answer is (A).