Previous Year Paper
CAT2007Previous Years Paper
Cities A and B are in different time zones. A is located
3000 km east of B. The table below describes the schedules of an airline operating nonstop flights between A and B. All the times indicated are local and on the same day.
Arrival
Departure 
Arrival 

City 
Time 
City 
Time 
B 
8:00 am 
A 
3:00 pm 
A 
4:00 pm 
B 
8:00 pm 
Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced by a steady wind blowing from east to west at 50 km per hour.
What is the plane’s cruising speed in km per hour?
A  600

B  500

C  700

D  550

E  Cannot be determined

Let the speed of the plane be x km/h
Then its speed from B to A = (x + 50) km/ h
and its speed from A to B = (x – 50) km/ h
The fight starts from city B (8.00 am) and arrives at city B (8.00 am) after taking a halt for 1 hour in city A
Therefore Total time taken = 11 hours
â 11x^{2} – 6000x – 27500 = 0
Solving the quadratic equation, x = 550
Therefore, time taken from B to A = =6
Flight reaches A when local time at B is 2.00 p.m. which is same as local time 3.00 p.m. at A. Therefore, required time difference = 1 hour
Ans. D
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