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Q.

What is the minimum number of square marbles required to tile a floor of length 5 metres 78 cm and width 3 metres 74 cm?

 A.

176

 B.

187

 C.

540

 D.

748

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Solution:
Option(B) is correct

The marbles used to tile the floor are square marbles.

Therefore, $\text{the length of the marble} = \text{width of the marble}.$

As we have to use whole number of marbles, the side of the square should a factor of both 5 m 78 cm and 3m 74. And it should be the highest factor of 5 m 78 cm and 3m 74.

5 m 78 cm = 578 cm and 3 m 74 cm = 374 cm.
The HCF of 578 and 374 = 34.

Hence, the side of the square is 34.

The number of such square marbles required,

$=  \dfrac{578×374}{34×34}$
$=  17×11=$ 187 marbles


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