A Question is given followed by two Statements I and II. Consider the Question and the Statements.

A person buys three articles p, q and r for ` 50. The price of the article q is ` 16 which is the least.

Question: What is the price of the article p?

Statement-I : The cost of p is not more than that of r.

Statement-II: The cost of r is not more than that of p.

Which one of the following is correct in respect of the above Question and the Statements?

The correct option is: The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

Step-by-Step Analysis:
Let the prices of the three articles p, q, and r be represented by $p$, $q$, and $r$ respectively.
From the given information:
1. The total cost of the three articles is ` 50. Therefore, we have the equation:
$p+q+r=50$
2. The price of article q is ` 16, which is the least price among all three articles.
So, $q=16$, and since it is the least, both $p$ and $r$ must be greater than or equal to 16 (i.e., $p\ge 16$ and $r\ge 16$).

Substituting $q=16$ into our equation:
$p+16+r=50$
$p+r=50-16$
$p+r=34$

Now let's analyze the statements to see if we can find the unique price of article p:

Using Statement-I alone:
Statement-I says: "The cost of p is not more than that of r."
This mathematically translates to:
$p\le r$
Since $p+r=34$ and $p\ge 16$ (since $q=16$ is the least), there can be multiple integer values for $p$ and $r$. For example:
- If $p=16$, then $r=18$ (satisfies $p\le r$ and $p\ge 16$)
- If $p=17$, then $r=17$ (satisfies $p\le r$ and $p\ge 16$)
Since we cannot find a unique value for $p$, Statement-I alone is not sufficient.

Using Statement-II alone:
Statement-II says: "The cost of r is not more than that of p."
This mathematically translates to:
$r\le p$
Using $p+r=34$ and $r\ge 16$ (since $q=16$ is the least), we again have multiple possibilities:
- If $r=16$, then $p=18$ (satisfies $r\le p$ and $r\ge 16$)
- If $r=17$, then $p=17$ (satisfies $r\le p$ and $r\ge 16$)
Since we cannot find a unique value for $p$, Statement-II alone is also not sufficient.

Using both Statement-I and Statement-II together:
From Statement-I, we have:
$p\le r$
From Statement-II, we have:
$r\le p$
For both inequalities to hold simultaneously, we must have:
$p=r$
Substituting $r=p$ into the equation $p+r=34$:
$p+p=34$
$2p=34$
$p=17$
This gives us a unique price of ` 17 for article p.

Thus, the question can be answered by using both statements together, but cannot be answered using either statement alone.