Question

What will be the total cost of creating a 1-foot border of tiles along the inside edges of a room?
I. The room is $48$ feet in length and $50$ feet in breadth.
II. Every tile costs Rs. $10$.

• A. If the question can be answered with the help of statement I alone.
• B. If the question can be answered with the help of statement II alone.
• C. If both statements I and II are needed to answer the question.
• D. If the question cannot be answered even with the help of both statements.

Hint:

In border tiling problems, subtract the inner rectangle area from the outer to get the border area. Always check if tile size is given or can be assumed.

Answer 1

The Correct Option is C

We are tasked with finding the total \emph{cost} of creating a 1-foot wide border of tiles along the inside edges of a room.
This border is effectively the difference in area between the outer rectangle (full floor) and the inner rectangle (after removing 1-foot border from all sides).

Step 1: From Statement I
Room length = $48$ ft, breadth = $50$ ft.
Outer area: \[ A_{\text{outer}} = 48 \times 50 = 2400 \ \text{sq. ft} \] Inner dimensions = $(48 - 2)$ ft $\times$ $(50 - 2)$ ft = $46 \times 48$ ft.
Inner area: \[ A_{\text{inner}} = 46 \times 48 = 2208 \ \text{sq. ft} \] Border area: \[ A_{\text{border}} = A_{\text{outer}} - A_{\text{inner}} = 2400 - 2208 = 192 \ \text{sq. ft} \] So Statement I gives the total area of the border. But without the cost per tile or tile size, we cannot find the total cost. Hence Statement I alone is not sufficient.

Step 2: From Statement II
Every tile costs Rs. 10. But without knowing how many tiles are needed (or area covered), we cannot find the total cost. Hence Statement II alone is not sufficient.

Step 3: Combining Statements I and II
From Statement I, we know the area = $192$ sq. ft. Assuming each tile covers $1$ sq. ft (standard assumption unless otherwise stated), the number of tiles required = $192$.
From Statement II, cost per tile = Rs. 10.
Total cost: \[ \text{Total Cost} = 192 \times 10 = \text{Rs. }1920 \] Thus, both statements together are sufficient.