Mother and daughter — Problems on Ages Aptitude Question
Mother and daughter: The sum of the ages of a mother and her daughter is 50. Five years ago the mother was seven… Answer and worked solution on CodeKairo.
- Topic: Problems on Ages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
The sum of the ages of a mother and her daughter is 50. Five years ago the mother was seven times as old as the daughter. How old is the mother now?
Options
- 35
- 38
- 40
- 45
Show the answer and the worked solution
Correct answer: C. 40
Worked solution
- Daughter = d, mother = 50 − d.
- Five years ago: 45 − d = 7(d − 5) = 7d − 35 → 8d = 80 → d = 10.
- Mother = 50 − 10 = 40.
- Check: 35 = 7 × 5. ✓
Answer: 40.
The idea
Use the sum to express one age through the other, so the 'years ago' condition becomes a single equation.
Shortcut. Five years ago the ages summed to 50 − 10 = 40, split 7 : 1 into 35 and 5; the mother is now 35 + 5 = 40.
Common trap. 35 — the mother's age five years ago, given without adding the 5 years back.