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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.

Common Information Question: 1/3

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

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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 $p=63$

$\Rightarrow q =72$


(1) Comment(s)


Parag
 ()

no insects left after last day so

$8p-7q = 0$

$8\times 63 -7q = 0$

$7q = 504$

$q = 72$