Exams › IBPS PO › Quantitative Aptitude

There are only three people in a family: father, mother, and a child. If the present ages of the father and mother are in the ratio 10:9, respectively, then find the present age of the child. Statement I: Ten years hence, the child's age will be 56% less than that of the father. Statement II: The child's present age is 70% less than that of the father and 24 years less than that of the mother. Statement III: Six years ago, the mother's age was 5 times the child's age. Six years hence, the father's age will be 28 years more than the child's age. Statement IV: The difference between the present ages of the mother and father is 4 years, and the difference between the present ages of the child and mother is 24 years.

1. Only I
2. Only II
3. Only I, II and III
4. Only II, III and IV

Correct answer: Only II, III and IV

Solution

The father and mother ages are in the ratio 10:9, so their difference is 1 part. Statement II directly gives the child's age relative to both parents, and Statements III and IV also allow a unique solution. Statement I alone does not uniquely determine the child's age, so the correct choice is Only II, III and IV.

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