# Q. A rectangular floor measures 4 m in length and 2.2 m in breadth. Tiles of size 140 cm by 60 cm have to be laid such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. What is the maximum number of tiles that can be accommodated on the floor?

(a) 6

(b) 7

(c) 8

(d) 9

Correct Answer: (c) 8

Official Answer by UPSC is (d) 9

#### Question from UPSC Prelims 2023 CSAT

**Explanation : **

## Maximum Tiles on Rectangular Floor

First, we need to convert the measurements of the floor and the tiles into the same units. Since the tiles are measured in centimeters, we’ll convert the floor measurements to centimeters.

1 meter = 100 centimeters

So, the floor measures 400 cm in length and 220 cm in breadth.

Next, we need to find out how many tiles can fit along the length and the breadth of the floor.

For the length: 400 cm / 140 cm = 2.857 tiles. We can’t have a fraction of a tile, so we can fit 2 tiles along the length.

For the breadth: 220 cm / 60 cm = 3.666 tiles. Again, we can’t have a fraction of a tile, so we can fit 3 tiles along the breadth.

However, we can also try to fit the tiles in the other orientation.

For the length: 400 cm / 60 cm = 6.666 tiles. We can fit 6 tiles along the length.

For the breadth: 220 cm / 140 cm = 1.571 tiles. We can fit 1 tile along the breadth.

So, we can either fit 2 tiles along the length and 3 tiles along the breadth for a total of 2*3 = 6 tiles, or we can fit 6 tiles along the length and 1 tile along the breadth for a total of 6*1 = 6 tiles.

However, if we look closely, we can see that there is some space left over when we fit 2 tiles along the length and 3 tiles along the breadth. The length of the floor is 400 cm, and 2 tiles take up 2*140 cm = 280 cm. This leaves 400 cm – 280 cm = 120 cm of space, which is enough for another tile if we place it in the 60 cm orientation. Similarly, the breadth of the floor is 220 cm, and 3 tiles take up 3*60 cm = 180 cm. This leaves 220 cm – 180 cm = 40 cm of space, which is not enough for another tile.

So, by placing 2 tiles along the length and 3 tiles along the breadth, and then adding 2 more tiles in the space left over, we can fit a total of 2*3 + 2 = 8 tiles on the floor.

Therefore, the correct answer is (c) 8.