UPSC Prelims 2023 · CSAT
Question 67: Basic Numeracy
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 ?
AnswerUPSC’s answer is (d).
The floor is 400 x 220 cm and a tile is 140 x 60 = 8400 sq cm, so area alone allows 10. But 220 cannot be made exactly from 140s and 60s (the best is 140 + 60 = 200), so every 1 cm strip across the width wastes at least 20 cm. Usable area is at most 400 x 200 = 80000, so at most 9 tiles. Nine fit as a pinwheel: two upright tiles bottom left, two flat tiles along the bottom to their right, two upright tiles top right, two flat tiles along the top to their left, and one flat tile in the middle.
Why each option is right or wrong
- (a) Wrong: nine tiles fit.
- (b) Wrong: nine tiles fit.
- (c) Wrong: a simple row layout gives 8, but the pinwheel fits a ninth.
- (d) Right: 9 fit, and the 200 cm limit rules out 10.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.