[From CAT 1997] A certain race is made up of three stretches: A, B and C, each 2 km long, and to be

#bprep #cat1997_bprep
A certain race is made up of three stretches: A, B and C, each 2 km long, and to be covered by a certain mode of transport. The following table gives these modes of transport for the stretches, and the minimum and maximum possible speeds (in km/hr) over these stretches. The speed over a particular stretch is assumed to be constant. The previous record for the race is 10 min.

Min. Max.
A Car 40 60
B Motor-cycle 30 50
C Bicycle 10 20

1. Anshuman travels at minimum speed by car over A and completes stretch B at the fastest speed. At what speed should he cover stretch C in order to break the previous record?
A) Maximum speed for C
B) Minimum speed for C
C) This is not possible
D) None of these

2. Mr Tortoise completes the race at an average speed of 20 km/hr. His average speed for the first two stretches is four times that for the last stretch. Find the speed over stretch C.
A) 15 km/hr
B) 12 km/hr
C) 10 km/hr
D) This is not possible

3. Mr Hare completes the first stretch at the minimum speed and takes the same time for stretch B. He takes 50% more time than the previous record to complete the race. What is Mr Hare's speed for the stretch C?
A) 10.9 km/hr
B) 13.3 km/hr
C) 17.1 km/hr
D) None of these

This question was asked in CAT 1997 examination.