Question

Geeta planned to floor her living room of size $520\text{cm}\times 300$ cm with the least number of square tiles of equal areas. If the cost for tiling is ₹ 64/tile, find the total cost incurred on tiling.

• A. ₹ 18,000
• B. ₹ 24,960
• C. ₹ 15,600
• D. ₹ 18,200

Answer 1

The correct option is B ₹ 24,960

First we need to find the side length of largest square tile which can be used to floor the rectangular living room of size $520\times 300$ cm.

HCF of 520 and 300 gives the side length of the largest square.
$520=300\times 1+220$
$300=220\times 1+80$
$220=80\times 2+60$
$80=60\times 1+20$
$60=20\times 3+0$
The HCF of 520 and 300 is 20.
$\Rightarrow$ The area of the square tile is $20\times 20=400{\text{cm}}^2.$

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

So, the cost of purchasing the square tiles is $390\times ₹64=₹24,960.$