MBA Exam

A steamer capable of going at upto 12 km/hr in still water, carries passengers and shuttles between Nagarjuna Konda (NK) and Nagarjuna Dam(ND), which is 10 km upstream of NK. One day it starts from NK at an upstream speed of 2 km/hr. After 1 hour the crew realizes that there is a hole in the steamer and water has been entering it at a rate of two kilo gallons/hour from the beginning of the trip. As soon as 6 kilo gallons of water enter the steamer, it starts sinking. What is the minimum still-water speed (in km/hr) should the steamer maintain so that it reaches ND and returns to NK before it starts sinking given that the speed of the water current is 1 km/hr?

1) 8
2) 8.5
3) 9
4) 9.5

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MBA Other Question
In ΔABC, D is the midpoint of BC. E is a point on AC such that AE :
EC = 2 : 1 and F is a point on AB such that AF : FB = 3 : 1. Line
segments AD and FE intersect at point O. What is the ratio of the area
of ΔDOF to the area of ΔDOE?

1) 3:4
2) 9:8
3) 8:9
4) none
 Petya's mother sends him to the market with a red and green bag to buy 10 carrots and 6 radishes.On the way home, Petya distributes the vegetables into 2 bags in such a way that no bag is empty .In how ways can he can do this?

1) 60
2) 75
3) 76
4) 77