- A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
- B. The Question can be answered by using either Statement alone
- C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- D. The Question cannot be answered even by using both the Statements together
Answer: C
Explanation
We are given: p + q + r = ₹50 and q = ₹16. We also know that q is the least price, so p ≥ 16 and r ≥ 16.
Substituting q=16 into the total cost equation: p + 16 + r = 50 => p + r = 34.
**Statement I: The cost of p is not more than that of r.** This means p ≤ r.
Given p+r=34 and p,r ≥ 16:
– If p=16, then r=18. This satisfies p ≤ r (16 ≤ 18).
– If p=17, then r=17. This satisfies p ≤ r (17 ≤ 17).
Since p could be 16 or 17, Statement I alone is insufficient to find a unique value for p.
**Statement II: The cost of r is not more than that of p.** This means r ≤ p.
Given p+r=34 and p,r ≥ 16:
– If p=18, then r=16. This satisfies r ≤ p (16 ≤ 18).
– If p=17, then r=17. This satisfies r ≤ p (17 ≤ 17).
Since p could be 17 or 18, Statement II alone is insufficient to find a unique value for p.
**Combining Statement I and Statement II:**
From Statement I, p ≤ r.
From Statement II, r ≤ p.
The only way both conditions can be true simultaneously is if p = r.
Substitute p = r into the equation p + r = 34:
p + p = 34 => 2p = 34 => p = 17.
Since p=17, then r=17. Both are indeed greater than or equal to q=16. Thus, the price of article p is uniquely determined as ₹17.
Therefore, both statements together are sufficient. This question tests data sufficiency and basic algebraic problem-solving.