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?
Answer & explanation
Answer: (d) 9
Any line across the 220 cm breadth meets tile sides of 60 cm or 140 cm, which can cover at most 200 cm of it. So at most 400 × 200 = 80,000 cm² can be tiled, room for fewer than 10 tiles of 8,400 cm², and a staggered layout fits 9.
- Floor = 400 cm × 220 cm; one tile = 140 cm × 60 cm = 8,400 cm².
- Across the 220 cm breadth, tile sides add up in 60s and 140s: the best totals are 60 + 140 = 200 and 60 + 60 + 60 = 180. So every line across the breadth leaves at least 20 cm uncovered.
- Covered area ≤ 400 × 200 = 80,000 cm², so tiles ≤ 80,000 ÷ 8,400 ≈ 9.5, i.e. at most 9.
- A layout of 9 (length measured 0–400, breadth 0–220): three tiles lying lengthwise, stacked, at length 0–140 (breadth 0–180); one lengthwise tile at length 140–280, breadth 0–60; two standing tiles (60 along the length) at length 140–260, breadth 60–200; two standing tiles at length 280–400, breadth 0–140; one lengthwise tile at length 260–400, breadth 140–200.
- 3 + 1 + 2 + 2 + 1 = 9 tiles, none overlapping — the maximum.
Remember · For tiling maxima, check a 'line' bound as well as area: the lengths that fit across a side often beat the area estimate.
Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·