Question

A carpenter constructs two boxes A and B. What is the volume of B?
Statement 1: Volume of A is 16 m³
Statement 2: Length, Breadth and height of B is twice that of A

• A. Statement (1) alone is sufficient to answer the question
• B. Statement (2) alone is sufficient to answer the question
• C. Both the statements together are needed to answer the question
• D. Either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. Neither statement (1) nor statement (2) suffices to answer the question

Answer 1

The Correct Option is C

To find the volume of Box B, we need to evaluate the given statements:

Statement 1: Volume of A is 16 m³.

This statement gives us information about the volume of Box A but provides no direct information about Box B. Alone, this statement is insufficient to determine the volume of Box B.

Statement 2: Length, breadth, and height of B are twice that of A.

This statement gives us a relationship between the dimensions of Boxes A and B but does not provide the actual dimensions or volume of Box A. Alone, this statement is insufficient to determine the volume of Box B.

Combining Both Statements:

From Statement 1, we know that the volume of Box A is \(16 \, \text{m}^3\).

Let the dimensions of Box A be \(l\) (length), \(b\) (breadth), and \(h\) (height). Therefore, the volume of Box A is given by:

l \times b \times h = 16\.

From Statement 2, the dimensions of Box B are twice the dimensions of Box A; thus, they are \(2l\), \(2b\), and \(2h\).

The volume of Box B is then:

(2l) \times (2b) \times (2h)\.

Simplifying this, we get:

= 8 \times (l \times b \times h)\.

Using the volume of Box A:

= 8 \times 16 = 128 \, \text{m}^3\.

Thus, the volume of Box B is \(128 \, \text{m}^3\).

Therefore, both statements together are needed to answer the question. This justifies the correct answer:

Both the statements together are needed to answer the question.