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Q67·CSAT · Prelims 2023

Fitting tiles on a rectangular floor

ReasoningMensuration (2D)Cube & geometry● Hard

Question

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?

Options

a

6

b

7

c

8

Answer
d

9

Explanation

Convert all physical measurements into a single uniform unit (centimeters): Floor length = 4 m = 400 cm. Floor width = 2.2 m = 220 cm. Tile dimensions = 140 cm × 60 cm.

Let's test geometric configurations to maximize fit: Try orienting the tiles such that their 140 cm lengths align along the floor's 400 cm side:

Along length: 400 \div 140 = 2 tiles, leaving a 400 - 280 = 120 cm remaining gap.
Along width: 220 \div 60 = 3 tiles, leaving a 220 - 180 = 40 cm remaining gap.

This primary block grid layout fits exactly 2 × 3 = 6 tiles.

Now, optimize the remaining unutilized corner gaps (120 cm × 220 cm or 400 cm × 40 cm): Inside the 120 cm × 220 cm section, rotate the tiles so their 60 cm side faces the 120 cm gap edge:

Along the 120 cm gap: 120 \div 60 = 2 tiles.
Along the 220 cm side: 220 \div 140 = 1 tile.

This secondary rotated block fits exactly 2 × 1 = 2 more tiles.

Total combined tiles = 6 (primary grid) + 2 (rotated side extension) = 8 tiles.

In geometric packing problems, a simple area division matrix (Area₍floor₎ / Area₍tile₎) provides only a loose upper bound; you must manually partition the grid to account for fractional remainder waste lines.

Answer: (c).

Question details

Year

2023

Paper

CSAT

Question

Q67

Section

Logical & Analytical Reasoning

Sub-topic

Mensuration (2D)

Type

Cube & geometry

Difficulty

Hard

Source hint

Spatial reasoning

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