**Question:**

A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the bathroom is 10 ft. by 8 ft. What would be the size in cinches of the tile required that has to be cut and how many such tiles are required?

**Solution:**

A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the bathroom is 10ft. by 8ft. We need to find the size in inches of the tile required that has to be cut and number of such tiles are required.

Size of bathroom = 10ft by 8ft

$=(10 \times 12)$ inch. by $(8 \times 12)$ inch

$=120$ inch. by 96 inch.

The largest size of tile required = H.C.F. of 120 and 96.

By applying Euclid’s division lemma

$120=96 \times 1+24$

$96=24 \times 4+0$

Therefore, H.C.F. = 24.

Thus, largest size of tile required = 24 inches.

Therefore,

No. of tiles required $=\frac{\text { Area of bathroom }}{\text { Area of } 1 \text { tile }}$

$=\frac{120 \times 96}{24 \times 24}$

$=5 \times 4$

$=20$ tiles