A hall 50 m long and 45 m broad is to be paved with square tiles. Find the largest tile as well as its number in the given options so that the tiles exactly fit in the hall :

A. 36 sq. m and 80 tiles

B. 16 sq. m and 80 tiles

C. 25 sq. m and 90 tiles

D. 36 sq. m and 90 tiles

Answer: Option C

Solution(By Examveda Team)

Length of hall = 50 m
Breadth of hall = 45 m
Area of hall = (50 × 45) m
Maximum length of a square tiles = HCF of 50 m and 45 m = 5 metres
Area of tiles = 5 × 5 = 25 sq. m
∴ Number of tiles :
$$\eqalign{ & = \frac{{50 \times 45}}{{25}} \cr & = 90{\text{ tiles}} \cr} $$