Aptitude Discussion

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 |

**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**