Question

Geeta planned to floor her living room of size 520 cm x 300 cm with the least number of square tiles of equal areas. If the cost for tiling is ₹ 64/tile, find the total cost (in ₹) incurred on tiling.

• A. 24960

Answer 1

The correct option is A 24960
First we need to find the side length of largest square tile which can be used to floor the rectangular living room of size 520 cm x 300 cm.

HCF of 520 and 300 gives the side length of the largest square.

By Euclid's Division Lemma,
$520=300\times 1+220$
$300=220\times 1+80$
$220=80\times 2+60$
$80=60\times 1+20$
$60=20\times 3+0$
The HCF of 520 and 300 is 20.

$\Rightarrow \text{The area of the square tile is}20\times 20=400{\text{cm}}^2.$

The number of tiles required to floor the living room 520 cm x 300 cm is given by:
$\text{Number of tiles}=\frac{520\times 300}{400}=390$

$\text{So, the total cost}=390\times ₹64=₹24,960.$