Three persons A, B and C are standing in a qu | vedclass

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Question

(C) To find the minimum number of persons, we consider the arrangement where the positions overlap as much as possible.Given: $3$ persons ahead of $C$

Vedclass · Accepted Answer

$28$

Vedclass · Answer

(C) To find the minimum number of persons, we consider the arrangement where the positions overlap as much as possible.Given: $3$ persons ahead of $C$, $8$ persons between $B$ and $C$, $5$ persons between $A$ and $B$, and $21$ persons behind $A$.Case $I$: Order $C, B, A$. Total $= 3 (	ext{ahead of } C) + 1 (C) + 8 (	ext{between } C, B) + 1 (B) + 5 (	ext{between } B, A) + 1 (A) + 21 (	ext{behind } A) = 40$.Case $II$: Order $C, A, B$. Since there are $8$ persons between $B$ and $C$ and $5$ between $A$ and $B$, the number of persons between $A$ and $C$ is $8 - 5 - 1 = 2$. Total $= 3 (	ext{ahead of } C) + 1 (C) + 2 (	ext{between } C, A) + 1 (A) + 21 (	ext{behind } A) = 28$.Comparing the two cases, the minimum number of persons is $28$.

Three persons $A, B$ and $C$ are standing in a queue. There are $5$ persons between $A$ and $B$ and $8$ persons between $B$ and $C$. If there are $3$ persons ahead of $C$ and $21$ persons behind $A$, what could be the minimum number of persons in the queue?

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