Q. For five children with ages a<b<c<d< e; any two successive ages differ by 2 years.
Question: What is the age of the youngest child?
Statement-1: The age of the eldest is 3 times the youngest.
Statement-2: The average age of the children is 8 years.
Which one of the following is correct in respect of the above Question and the Statements?
(a) The Question can be answered by using one of the Statements alone, but cannot. be answered using the other Statement alone.
(b) The Question can be answered by using either Statement alone.
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
(d) The Question cannot be answered even by using both the Statements together.
Correct Answer: (b) The Question can be answered by using either Statement alone.
Question from UPSC Prelims 2023 CSAT
Explanation :
Five Children’s Ages Analysis
Let’s consider each statement separately:
Statement-1: The age of the eldest is 3 times the youngest.
Since the ages of the children increase by 2 years successively, let’s denote the age of the youngest child as ‘a’. Then the ages of the other children would be a+2, a+4, a+6, and a+8. According to the statement, the age of the eldest child (a+8) is 3 times the age of the youngest child (a). This gives us the equation 3a = a+8. Solving this equation, we find that a = 4. Therefore, the age of the youngest child is 4 years old.
Statement-2: The average age of the children is 8 years.
The average age is the sum of the ages divided by the number of children. So, 5a+20 = 8*5. Solving this equation, we again find that a = 4. Therefore, the age of the youngest child is 4 years old.
In conclusion, each statement alone is enough to answer the question. Therefore, the correct answer is (b) The Question can be answered by using either Statement alone.
