GATE2018 EE: GA-10

Question

$P, Q, R, \text{and } S$ crossed a lake in a boat that can hold a maximum of two persons, with only one set of oars. The following additional facts are available.

1. The boat held two persons on each of the three forward trips across the lake and one person on each of the two return trips.
2. $P$ is unable to row when someone else is in the boat.
3. $Q$ is unable to row with anyone else except $R$.
4. Each person rowed for at least one trip.
5. Only one person can row during a trip.

Who rowed twice?

• A. $P$
• B. $Q$
• C. $R$
• D. $S$

Comments

Ans R
QR ans RS

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What is the use of this information, “and one person on each of the two return trips”? We are not using it anyway to find our answer.

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Given to get more surity of answer

Answer 1

1. $P$ is unable to row when someone else is in the boat.
2. Each person rowed for at least one trip.

These two statements mean that $P$ must return at least once. So, one return trip is by $P$ alone.

1. $Q$ is unable to row with anyone else except $R.$
2. This also means that $Q$ cannot come back since
   1. if $P$ comes back in first return, and $Q$ comes back in second, $P$ and $Q$ will be left for third forward trip which is not possible
   2. if $P$ comes back in second return, it means $Q$ must have come back in first return, which again means both $P$ and $Q$ are left for the final trip. 
3. Since $Q$ cannot come back, it means both $Q$ and $R$ must go together in the forward trip.

• Suppose $P,S$ goes first and $S$ rows.
• $P$ comes back and then $Q$ and $R$ returns with $Q$ rowing.
• $R$ comes back and takes $P$ with $R$ rowing.
• Other alternative is $Q$ and $R$ going first. 
• In both cases $R$ has to row twice.

Correct Option: C.

Answer 2

By going through the above criterion we can conclude the following statements

In the first forward trip, Q and R will go and on this trip, Q will row.

Now, R will come back on the 1st return trip and R will row.

In the 2nd forward trip, R and P will go and R will row.

Now, P will come back on the 2nd return trip and P will row.

In the 3rd forward trip, P and S will go and S will row.

So, R rowed Twice. option C)