Data sufficiency for finding an exact age using age differences and ratios
Question
Consider the Question and two Statements given below: Question: What is the age of Manisha? Statement-1: Manisha is 24 years younger than her mother. Statement-2: 5 years later, the ages of Manisha and her mother will be in the ratio 3:5. Which one of the following is correct in respect of the Question and the Statements?
Options
Statement-1 alone is sufficient to answer the Question
Statement-2 alone is sufficient to answer the Question
Both Statement-1 and Statement-2 are sufficient to answer the Question
Both Statement-1 and Statement-2 are not sufficient to answer the Question
Explanation
Let Manisha's age be M and her mother's age be Mo.
Statement 1 gives a linear difference equation: Mo - M = 24. Infinite pairs satisfy this (e.g., 10 and 34, or 20 and 44). Insufficient.
Statement 2 gives a future ratio equation: M + 5/Mo + 5 = 3/5. Without a second constraint, infinite pairs satisfy this. Insufficient.
Combine both statements: Substitute Mo = M + 24 directly into the ratio equation from Statement 2: M + 5/(M + 24) + 5 = 3/5 M + 5/M + 29 = 3/5 Cross-multiply to solve for M: 5(M + 5) = 3(M + 29) 5M + 25 = 3M + 87 2M = 62 \implies M = 31 Manisha's age is definitively 31. Because resolving this requires the unique intersection of both equations, both statements together are sufficient.
Answer: (c).
Question details
Year
2022
Paper
CSAT
Question
Q49
Section
Data Interpretation & Sufficiency
Sub-topic
Problems on Ages
Type
Factual single
Difficulty
Easy
Source hint
What is the age of Manisha?
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