QUESTION

CSAT

Medium

Maths

Prelims 2024

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?

Select an option to attempt

Explanation

Using Statement-I alone: Statement-I tells us that the cost of p is not more than that of r. This means prp \le r, but it does not provide a unique relationship between p, q, and r to determine the exact price of p. Therefore, Statement-I alone is insufficient.

Using Statement-II alone: Statement-II tells us that the cost of r is not more than that of p. This means rpr \le p, but again, it does not provide enough information to determine the exact price of p. Thus, Statement-II alone is also insufficient.

Combining both Statements: From Statement-I, we know prp \le r, and from Statement-II, we know rpr \le p. This means p=rp = r, and together with the information that the total cost of p, q, and r is ₹50, we can solve for p. Let p=rp = r, and since q costs ₹16, the total cost equation is: p+q+r=50p + q + r = 50, p+16+p=50p + 16 + p = 50, 2p=342p = 34, p=17p = ₹17.

Thus, combining both statements gives us a unique solution for the price of p.

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