Q69. A Question if 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?

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.