Tiling a rectangular floor

CAT 2005 Slot 1 · QA · Medium · Mensuration

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Rectangular tiles each of size 70 cm×30 cm70\text{ cm} \times 30\text{ cm} must be laid horizontally on a rectangular floor of size 110 cm×130 cm110\text{ cm} \times 130\text{ cm}, 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. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is

  1. A.

    4

  2. B.

    5

  3. C.

    6

  4. D.

    7

Answer

C

Explanation

Area of floor =110×130=14300 cm2= 110 \times 130 = 14300\text{ cm}^2. Area of one tile =70×30=2100 cm2= 70 \times 30 = 2100\text{ cm}^2. Maximum possible theoretical tiles =⌊14300/2100⌋=6= \lfloor 14300 / 2100 \rfloor = 6. We can place 6 tiles as follows: Place two 70×3070 \times 30 tiles vertically (70×6070 \times 60) and two horizontally in the remaining space, accommodating 6 tiles easily without overlap. Thus, maximum number of tiles is 6.

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