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?

(a) Statement-1 alone is sufficient to answer the Question
(b) Statement-2 alone is sufficient to answer the Question
(c) Both Statement-1 and Statement-2 are sufficient to answer the Question ✓ UPSC's answer
(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question

Why the answer is (c)

• Let Manisha's current age be M and her mother's current age be Mo.

• Statement-1 provides the equation: Mo = M + 24.

• Statement-2 provides the equation: (M + 5) / (Mo + 5) = 3 / 5.

• Substituting Mo from Statement-1 into Statement-2 gives: (M + 5) / (M + 24 + 5) = 3 / 5.

• Solving 5(M + 5) = 3(M + 29) yields 5M + 25 = 3M + 87, so 2M = 62 and M = 31.

• Since both statements are required to form a solvable system of equations, option (c) is correct.

Why the other options are wrong

(a) Statement-1 alone is sufficient to answer the Question: Statement-1 alone only gives the difference in ages, not the specific value of Manisha's age.
(b) Statement-2 alone is sufficient to answer the Question: Statement-2 alone provides a ratio involving two unknowns without a fixed difference, making it unsolvable for a unique age.
(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question: The combination of both statements provides two independent linear equations with two variables, which is sufficient to find a unique solution.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.