Question

Geeta planned to floor her living room of size $520\times 300$ cm with the least number of square tiles of equal areas. If the cost for the first 100 tiles are Rs 64.00/tile, Rs 50.00/tile for the next 100 tiles and Rs 40.00/tile for any number of tiles after the first 200, find the total cost incurred on tiling.

• A. Rs 18,000
• B. Rs 19,000
• C. Rs 15,600
• D. Rs 18,200

Answer 1

The correct option is B Rs 19,000

Step 1:

Find the side length of largest square which tile 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 & 300 is 20.

Step 2:
The number of tiles required to floor the living room $(520\times 300)$ cm :
Number of tiles = $\frac{(520\times 300)}{(20\times 20)}$
Number of tiles = 390

Step 3:
So, the cost of purchasing the square tiles :
First 100 tiles cost Rs. 64.00/tile
Cost = $100\times 64$ = Rs 6400
Next 100 tiles cost Rs 50.00/tile
Cost = $100\times 50$ = Rs 5000
There are 390 tiles in total, Any number of tile more than 200 tiles in the order cost Rs 40/tile
Cost = $190\times 40$ = Rs 7600
Therefore, the total cost = Rs 6400+ 5000+ 7600 = Rs 19,000.