Consider the Question and two Statements given below:
Question : What is the age of Manisha?
Which one of the following is correct in respect of the Question and the Statements?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.
(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 Statement-2 are not sufficient to answer the Question
Solution:
Statement-2 alone is not sufficient to answer the question, but if taken together with Statement-1, the age of Manisha can be determined.
Let's assume the age of Manisha's mother as M.
From Statement-1, we know that Manisha is 24 years younger than her mother, so Manisha's age can be expressed as (M - 24).
Now, according to Statement-2, 5 years later, the ratio of Manisha's age to her mother's age will be 3:5. So, we can write:
(M - 24 + 5) : (M + 5) = 3 : 5
Simplifying this equation, we get:
3(M + 5) = 5(M - 19)
3M + 15 = 5M - 95
110 = 2M
M = 55
So, we know that Manisha's mother is 55 years old. Using Statement-1, we can find Manisha's age:
Manisha's age = Mother's age - 24 Manisha's age = 55 - 24 Manisha's age = 31
Therefore, the age of Manisha is 31 years.
In conclusion, Statement-2 alone does not provide enough information to determine Manisha's age, but when combined with Statement-1, we can calculate the age of Manisha.
So, final answer is (c).