Question

A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the bathroom is $10ft.by8ft.$ What would be size in inches of the tile required that has to be cut and how many such that tiles are required ?

Answer 1

Given:-

Size of bathroom $=\text{10ft. by 8ft.}$

As we know that,

$\text{1 ft.}=\text{12 inches}$

Therefore,

Size of the bothroom $=(10\times 12)\text{inch by}(8\times 12)\text{inch}=\text{120 inch by 96 inch}$

The largest size of tile required $=\text{HCF of 120 and 96}$

By applying Euclid’s division lemma

$120=96\text{1}+24$

$96=24\times 4+0$

$\therefore \text{HCF}=24$

$\therefore$ Largest size of tile required $=24\text{inches by}24\text{inches}$

Now,

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

$\therefore$ No. of tiles required $=\frac{120\times 96}{24\times 24}$

$\Rightarrow$ No. of tiles required $=5\times 4=20\text{tiles}$

Thus the no. of tiles required is $24$.

Hence the correct answer is $24\text{tiles}$.