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?

The correct option is Both Statement-1 and Statement-2 are sufficient to answer the Question.

Let us analyze the problem step-by-step to understand why both statements together are required and sufficient to find the age of Manisha.

Let the present age of Manisha be $m$ years and the present age of her mother be $M$ years.

Step 1: Analyzing Statement-1
According to Statement-1, Manisha is 24 years younger than her mother. We can write this relationship as the following equation:
$M-m=24$
Since we have one linear equation with two variables ($m$ and $M$), we cannot find a unique value for Manisha's age, $m$, using Statement-1 alone. Therefore, Statement-1 alone is not sufficient.

Step 2: Analyzing Statement-2
Statement-2 states that 5 years later, the ratio of the ages of Manisha and her mother will be 3:5.
Five years from now, Manisha's age will be $m+5$ and her mother's age will be $M+5$. The ratio of their ages can be written as:
$\frac{m+5}{M+5}=\frac{3}{5}$
Cross-multiplying, we get:
$5(m+5)=3(M+5)$
$5m+25=3M+15$
$5m-3M=-10$
Again, this is a single equation with two variables. We cannot determine a unique solution for $m$ using Statement-2 alone. Therefore, Statement-2 alone is not sufficient.

Step 3: Combining Statement-1 and Statement-2
When we combine both statements, we obtain a system of two linear equations with two variables:
Equation (1): $M=m+24$
Equation (2): $5m-3M=-10$
Substituting Equation (1) into Equation (2):
$5m-3(m+24)=-10$
$5m-3m-72=-10$
$2m=62$
$m=31$
Thus, by using both statements together, we can uniquely determine that Manisha's present age is 31 years. Therefore, both Statement-1 and Statement-2 are sufficient to answer the Question.