Q. 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?

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 the Statements using both together, but cannot be answered using either Statement alone

d) The Question cannot be answered even by using both the Statements together

Correct answer: c) The Question can be answered by the Statements using both together, but cannot be answered using either Statement alone

##### Question from UPSC Prelims 2024 CSAT Paper

**Explanation:**

## Person buys three articles p, q and r for 50

Let’s approach this step-by-step:

1. From the given information, we know:

– Total cost of p + q + r = 50

– Cost of q = 16 (which is the least)

2. We need to find the price of article p.

3. Let’s examine the statements:

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.

4. Analysis:

– Statement I alone doesn’t give us the exact price of p.

– Statement II alone doesn’t give us the exact price of p either.

– When we combine both statements, we can conclude that the cost of p is equal to the cost of r.

5. Using this information:

p + r + 16 = 50

2p + 16 = 50 (since p = r)

2p = 34

p = 17

Therefore, we can determine the price of p (17) only by using both statements together.

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