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
d. Both Statement-1 and Statcment-2 are not sufficient to answer the Question
Correct Answer: c. Both Statement-1 and Statement-2 are sufficient to answer the Question

Question from UPSC Prelims 2022 CSAT Paper

Explanation :

To determine the age of Manisha, we need to analyze both statements together.

Statement-1: Manisha is 24 years younger than her mother.
Let Manisha’s age be M and her mother’s age be X. So, X = M + 24.

Statement-2: 5 years later, the ages of Manisha and her mother will be in the ratio 3:5.
In 5 years, Manisha’s age will be M + 5 and her mother’s age will be X + 5. The ratio of their ages at that time will be 3:5.
(M + 5) / (X + 5) = 3 / 5

Now, we have two equations with two variables:

X = M + 24
(M + 5) / (X + 5) = 3 / 5
Substitute the value of X from the first equation into the second equation:
(M + 5) / (M + 24 + 5) = 3 / 5

Solve for M:
5(M + 5) = 3(M + 29)
5M + 25 = 3M + 87
2M = 62
M = 31

Manisha’s age is 31. Therefore, both Statement-1 and Statement-2 are sufficient to answer the question. The correct answer is:

c. Both Statement-1 and Statement-2 are sufficient to answer the Question