IIFT 2014 Question Paper Question 107

Question 107

A ferry carries passengers to Rock of Vivekananda and back from Kanyakumari. The distance of Rock of Vivekananda from Kanyakumari is 100km. One day, the ferry started for Rock of Vivekananda with passengers on board, at a speed of 20 km per hour. After 90 minutes, the crew realized that there is a hole in the ferry and 15 gallons of sea water had already entered the ferry. Sea water is entering the ferry at the rate of 10 gallons per hour. It requires 60 gallons of water to sink the ferry. At what speed should the driver now drive the ferry so that it can reach the Rock of Vivekananda and return back to Kanyakumari just in time before the ferry sinks? (Current of the sea water from Rock of Vivekananda to Kanyakumari is 2km per hour.)

Solution

The ferry must have traveled 1.5*(20-2) = 27 kms already. The ferry needs to cover 73 kms to reach Rock of Vivekananda and 100 kms back to Kanyakumari. 15 gallons of water has already entered the ship. 45 more gallons will enter in order for the ship to sink. So it takes 4.5 hours. The ferry has to travel 70 km and return 100 km before it sinks. Speed of stream from Rock memorial to Kanniyakumari is 2 km/hr

Check the options.

Option 1: $$\frac{73}{38}+\frac{100}{41} = 4.36$$
Option 2: $$\frac{73}{39}+\frac{100}{40} = 4.37$$
Option 3 : $$\frac{73}{40}+\frac{100}{38} = 4.46$$
Option 4: $$\frac{73}{33}+\frac{100}{41} = 4.65$$
Thus, the closest option is option C.
Hence, option C is the correct answer.



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