Aptitude - Area - Discussion

@All.

If we want to get the least number of tiles, the largest tiles must be used. This is why hcf is used. If you want to get the most number of tiles, then, the smallest tiles will be used, which is lcm.

1m=100 Cms, so convert 15meters *100=1500+17cms=1571,
Like wise 9meters*100=900+2cms=902cms.

@Tina.

The dimensions of the room is 1517cm X 902cm.
Square tiles of the same side are only to be used. So dimensions of the square tiles should not be in integral metres. Since no. of square tiles to be paved are whole numbers, 1517 and 902 should be divisible by a number which gives the number of square tiles to be paved along length and breadth.
Thus hcf is used.
Area of room / Area of 1 tile = No. of tiles.
= ( 1517 X 902 ) / ( 41 X 41 ) = 37 X 22 = 814 tiles.

902)1517(1
902
------
615)902(1
615
---
287)615(2
574
---
41)287(7
287
---
0

By this method of successful division, remainder goes 0. Last divisor forms your req. HCF....

So 41 is ur HCF :-)

Here 41 * 37=1517 and 41 * 22=902.

So, 41 comes in both the no. (which is called hcf).
Now the area of the floor is 1512 * 902.
So least no. of tiles to cover the floor = n * 41^2 (as square tile can be taken of length 41).
Therefore n =37*22 =814.

How you got 1517 and 902? Please explain.

Thanks for your explanation of HCF @Ibrahimsha.

Why we use HCF here?

We need that size of square which must occupy the entire space. If we take side of some other square, then 100% some space gona left as we can't bread the last tile. If we take the hcf, then we can get the side of square which is divisible by length and breadth both exactly.

Thanks @Ibrahimsha.