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: 90 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. What is the mother's present age?
Options
- 35
- 38
- 40
- 45
Show the answer and the worked solution
Correct answer: C. 40
Worked solution
- Daughter = d, mother = 50 − d.
- 45 − d = 7(d − 5) = 7d − 35 → 8d = 80 → d = 10.
- Mother = 50 − 10 = 40.
- Check: five years ago 35 and 5. ✓
Answer: 40.
The idea
Use the sum to express one age through the other so that only one variable survives into the 'years ago' condition.
Shortcut. Five years ago the sum was 50 − 10 = 40, split 7 : 1 into 35 and 5. Add the five years back: the mother is 40.
Common trap. 35 is the mother's age five years ago; splitting 40 in the ratio 7 : 1 and stopping there, without adding the five years back, produces it.