UPSC Prelims 2022·CSAT·Quantitative Aptitude·Arithmetic

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?

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  1. AStatement-1 alone is sufficient to answer the Question
  2. BStatement-2 alone is sufficient to answer the Question
  3. CBoth Statement-1 and Statement-2 are sufficient to answer the QuestionCorrect
  4. DBoth Statement-1 and Statement-2 are not sufficient to answer the Question

Explanation

Here's a brief explanation: 1. Statement 1 alone: "Manisha is 24 years younger than her mother." This gives a relationship between their ages (M = Mother's age - 24) but doesn't provide specific numerical values. It's one equation with two unknowns, so it's not sufficient. 2. Statement 2 alone: "5 years later, the ages of Manisha and her mother will be in the ratio 3: 5." This gives another relationship ((M+5) / (Mother's age + 5) = 3/5) but again doesn't provide specific numerical values. It's also one equation with two unknowns, so it's not sufficient. 3. Both Statements together: When combined, we have two independent equations with two variables (Manisha's age and her mother's age). * From S1: Manisha's age = Mother's age - 24 * From S2: 5 * (Manisha's age + 5) = 3 * (Mother's age + 5) These two equations can be solved simultaneously to find a unique value for Manisha's age. Therefore, both statements together are sufficient to answer the question. The final answer is C because neither statement alone is sufficient, but both statements combined provide enough information to determine Manisha's age.
Quantitative Aptitude: Consider the Question and two Statements given below: Question: What is the age of Manisha? Statement- 1: Manisha is 24

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