A Question is given followed by two Statement 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 Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
To determine the price of article p using the given information, let's analyze both the question and statements:
Given Information:
- Total cost of articles p, q, and r is ₹50.
- The price of article q is ₹16, which is the least among the three articles.
Based on the given information, the equation for the total cost is:
\(p + q + r = 50\)
Substituting the value of q:
\(p + 16 + r = 50\)
Simplifying, we get:
\(p + r = 34\)
Using the Statements:
Statement I:
The cost of p is not more than that of r.
This implies:
\(p \leq r\)
Statement II:
The cost of r is not more than that of p.
This implies:
\(r \leq p\)
These two statements together imply \(p = r\).
Solution Using Both Statements:
With \(p = r\), substituting in the equation \(p + r = 34\) gives:
\(p + p = 34\)
Therefore:
\(2p = 34\)
Solving for p:
\(p = \frac{34}{2} = 17\)
Conclusion:
The price of article p is ₹17. Thus, the question can be answered by using both statements together, but cannot be answered using either statement alone, as only combining the two statements gives us the exact equality needed.
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