Question

The cost of plastering the four walls of a room is Rs. 25. The cost of plastering a room twice in length breadth and height will be
A) Rs. 50
B) Rs. 75
C) Rs. 100
D) Rs. 200

Answer 1

Hint: We are given the cost of plastering 4 walls of a room. It is given as Rs.25. The new length, breadth and height of the room are twice as before. The cost of plastering depends on the surface area. So we can calculate the ratio of the surface area using the equation for the lateral surface area of a cuboid. The same ratio can be used to find the new cost.

Complete step by step solution: We can draw a diagram of the room with length l, breadth b, and height h.

We know that plastering cost depends on the surface area. In this case, only 4 walls of the room are plastering. So, we take the lateral surface area. Let it be S. It is given by,
${\text{S = 2h}}\left( {{\text{l + b}}} \right)$ where l is the length of the room, b is the breadth of the room and h is the height of the room.
Let the new surface area when length, breadth and height is doubled be S’. Then l becomes 2l, b becomes 2b and h becomes 2h. Its surface area is given by,
\[{{\text{S}}^{\text{'}}}{\text{ = 2} \times \text{2h}}\left( {{\text{2l + 2b}}} \right){\text{ = 4} \times \text{2h}}\left( {{\text{l + b}}} \right){\text{ = 4S}}\]
From the above equation, we can understand that the surface area has increased 4 times. So the cost will also increase 4 times.
As the given cost is Rs. 25, the new cost will be 4 times Rs. 25,
New cost${{ = 4 \times 25 = 100}}$
Therefore, the new cost is Rs.100

So, the correct answer is option C.

Note: We only need to take the lateral surface area as it is mentioned 4 walls in the question. While working with problems related to area and volume, use proper units and conversions, if necessary. Drawing and marking the dimensions will be helpful for a better understanding of these types of questions. The equation of the lateral surface area can be derived by adding the area of 4 walls separately.