Aptitude Discussion

**Common Information**

A boy is roaming on the roof of his house observes that the insects are there in bunches. He found '$p$' insects on day 1. On day two, the number of insects doubled and he takes out '$q$' insects and kills them. On the third day again, the insects left is doubled and he again takes out '$q$' insects and kill them. On the fourth day also he found the same, insects left is doubled and he takes out '$q$' insects again. He is surprised to find that there are no insects left on his roof.

Q. |
If the number of insects on the roof, on day 1 is 63, then the number of insects that they kill on the fourth day is: |

✖ A. |
63 |

✖ B. |
90 |

✔ C. |
72 |

✖ D. |
75 |

**Solution:**

Option(**C**) is correct

Day (1) -> Number of insects $-> p$

Day (2) -> Number of insects $-> 2p−q$

Day (3) -> Number of insects $-> 4p−3q$

Day (4) -> Number of insects $-> 8p−7q$

$\Rightarrow P$ has to multiple of 7 so that $q$ is an integer

If $p=63$

$\Rightarrow q =72$

**Parag**

*()
*

no insects left after last day so

$8p-7q = 0$

$8\times 63 -7q = 0$

$7q = 504$

$q = 72$