Question:medium

A certain bottle can hold a maximum of how many litres of liquid?
Statement 1: The bottle currently contains 9 litres of liquid
Statement 2: If a litre of liquid is added to the bottle when it is half full of liquid, the amount of liquid in the bottle will increase by \(\frac{1}{3}\)

Updated On: Jan 13, 2026
  • Statement (1) alone is sufficient to answer the question
  • Statement (2) alone is sufficient to answer the question
  • Both the statements together are needed to answer the question
  • Either statement (1) alone or statement (2) alone is sufficient to answer the question
  • Neither statement (1) nor statement (2) suffices to answer the question
Show Solution

The Correct Option is C

Solution and Explanation

The correct answer is option (C):
Both the statements together are needed to answer the question

Let's analyze the problem. We want to find the maximum capacity of the bottle.

Statement 1: The bottle currently contains 9 litres of liquid. This tells us about the current amount, not the maximum capacity. Therefore, statement 1 alone isn't sufficient.

Statement 2: If a litre of liquid is added to the bottle when it is half full of liquid, the amount of liquid in the bottle will increase by 1/3. Let 'C' be the maximum capacity of the bottle. When the bottle is half full, it contains C/2 litres. Adding 1 litre increases the amount to C/2 + 1. The problem states that this increase represents a 1/3 increase in the amount of liquid. This isn't directly the final amount; instead, a more complex relationship is provided. This statement alone is also insufficient.

Now, consider both statements together. Let's revisit statement 2, focusing on the 1/3 increase. Let 'x' be the amount of liquid when the bottle is half full. Adding 1 litre increases the amount by 1/3. So, 1 = (1/3) * (the original amount when the bottle is half full). So we know when the bottle is half full, it contained 3 litres. Now we know, statement 2 reveals that when the bottle is half full, it contains 3 litres. Therefore the total capacity of the bottle is 6 litres.

By using both statements, we can set up the equation (C/2) + 1 = x + x/3 where x represents the liquid when the bottle is half full. And statement 2 says we can increase liquid to x + x/3, where the amount is 1 litre. With these two relations, we can solve for C. We now know that when bottle is half full, its 3 litres. We can find the capacity from there.

Therefore, both statements together are needed to answer the question.
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