The length and breadth ofa room are 15 m 17 cm and 9 m 2 cm respectively. How many, squarical tiles will cover the area of the floor of this room (minimum).

Options

A. 841
B. 820
C. 814
D. 840

Answer

C

Explanation

Given, length of the room = 15 m 17 cm =1517 cm
Breadth of the room = 9 m 2 cm = 902 cm
`therefore` Area of the floor of the room = `1517 xx 902 cm^2`
Since, square tiles are fitted on the floor of the room.
Hence, side of each square tile is equal to HCF of the length and breadth of the room.
`therefore` Side of the tile = HCF of 1517 and 902
`=41 (therefore 1517 = 37 xx 41` and `902 = 22 xx 41`}
`therefore` Area of one tile `=(41)^(2) = 1681 cm^(2)`
`therefore` Minimum number of square tiles which is fit
`=(1517 xx 902)/1681 = 814`