GATE EE 2018 Set 1 — Question 10
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Question
P, Q, R 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.
(i) 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.
(ii) P is unable to row when someone else is in the boat.
(iii) Q is unable to row with anyone else except R.
(iv) Each person rowed for at least one trip.
(v) Only one person can row during a trip.Who rowed twice?
(i) 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.
(ii) P is unable to row when someone else is in the boat.
(iii) Q is unable to row with anyone else except R.
(iv) Each person rowed for at least one trip.
(v) Only one person can row during a trip.Who rowed twice?
Correct answer
(C) R
Solution
Counting rowing turns. There are 3 forward trips and 2 return trips, i.e. 5 trips, each with exactly one rower. Four people each row at least once, so exactly one person rows twice ().What the constraints force.
1.P can row only when alone, so P can row only a return trip. For P to row back, P must first be carried across as a passenger, and must then be carried across again at the end. So P is a passenger on two forward trips.
2.Q can row only alone or with R. Q cannot row a return trip: whoever returns must cross forward again, but Q cannot be in one of P's two forward trips (P cannot row with company, and Q cannot row with P), so Q crosses forward only once, on the trip , which Q rows (R cannot be its rower, otherwise Q never rows).
3.So the forward trips are (Q rows), and , where row those trips. One return trip is rowed by P; the other return is by or (not Q, by step 2).
4.If S made the other return, S would cross forward twice, so both P-trips would be . Then R crosses only once, as a passenger with Q, and never rows, which violates (iv).
5.Hence R makes the other return and crosses forward twice: once with Q and once with P (rowing that trip, since P cannot row with someone else). The remaining forward trip is , rowed by S.
Rowing counts: P = 1 (a return), Q = 1 (), S = 1 (), R = 2 (a return and ).A valid schedule: cross (Q rows); R returns; cross (R rows); P returns; cross (S rows).Answer: R rowed twice.Continue learning with Success Tracker
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