Question

 In the following question below, 3 statements I, II and III are given. You are required to find out which of the given statement(s) is/are suffi cient to answer the question.How old was Deepa on October 2018 ?
I. Deepa is 6 yrs older than her sister Prabha
II. Prabha is 29 yrs younger than her mother
III. Deepa's mother celebrated her birthday on July 2018

• A. I and II
• B. All I, II and III
• C. II and III
• D. I and III

Answer 1

The Correct Option is B

To determine Deepa's age in October 2018, we need to analyze the information provided in each statement and determine which combination of these is sufficient to find the answer. 

1. From Statement I: "Deepa is 6 years older than her sister Prabha."
   • This statement alone gives the age relationship between Deepa and Prabha, but without Prabha's age, we cannot determine Deepa’s age.
2. From Statement II: "Prabha is 29 years younger than her mother."
   • This statement relates Prabha’s age to her mother’s age. Again, without knowing the mother's age or additional information, we cannot determine Deepa's age.
3. From Statement III: "Deepa's mother celebrated her birthday in July 2018."
   • This implies that we can mathematically express the ages but still does not give an actual age unless combined with other statements.

Let's now combine the statements:

• Combining Statements I, II, and III:
  • Suppose Deepa's mother's age in July 2018 is \( M \). Therefore, Prabha's age is \( M - 29 \).
  • From Statement I, Deepa’s age is \( (M - 29 + 6) = M - 23 \).

Since we know the timeline and the exact relationship between each person's age, with their mother's age as a reference from her birthday in July 2018, we can determine Deepa's age using all three statements. Without knowing \( M \), we specifically cannot calculate a numerical age, but these statements are definitely required together to establish a relationship correctly.

Conclusion: Hence, to determine Deepa's age, all three statements I, II, and III are necessary and sufficient. Therefore, the correct answer is: All I, II, and III.