Aptitude Discussion

Q. |
From a point $P$, on the surface of radius 3 cm, two cockroaches $A$ and $B$ started moving along two different circular paths, each having the maximum possible radius, on the surface of the sphere, that lie in the two different planes which are inclined at an angle of 45 degree to each other. If $A$ and $B$ takes 18 sec and 6 sec respectively, to complete one revolution along their respective circular paths, then after how much time will they meet again, after they start from $P$? |

✖ A. |
27 sec |

✖ B. |
24 sec |

✖ C. |
18 sec |

✔ D. |
9 sec |

**Solution:**

Option(**D**) is correct

Both the circular paths have the maximum possible radius hence, both have a radius of 3 cm each. Irrespective of the angle between the planes of their circular paths, the two cockroaches will meet again, at the point $Q$ only, which is diametrically opposite end of $P$.

$A$ will takes **9 seconds** to reach point $Q$, completing half a revolution.

On the other hand, $B$ would have completed \(\dfrac{3}{2}\) of his revolution and it will also reach point $Q$ simultaneously.