rn1112
A ship is travelling between two port cities with a speed such that it will reach its destination on time. After covering 25% of the distance, the ship faces an emergency and returns to its starting point with a different speed v. It then resumes travelling towards its destination without any further delay with the same speed v. By what percentage is v more than the original speed, if the ship reaches its destination in time?
A. 33.33
B. 50
C. 66.67
D. 75
E. 87.5
taken from CL GMAT
Let the total distance between the 2 ports be
4D.
Now,
25% of 4D = 1DLet the speed of the ship at the first half of the journey be
x when the ship travelled distance D and then returned because of an emergency.
If the emergency wouldn't have occurred, the rest of the distance would have been covered at speed
x only.Thus, 3D distance at speed x.
Time, in this case = 3D/x
Given that the speed after restarting the journey was
vSince, the ship will reach at the same time as before, it means that total distance 4D + D (while going back to the port) = 5D will be covered at speed v
Time, in this case = 5D/v
Both time are equal, so,
3D/x = 5D/v
v/x = 5/3
%= (v-x/x)*100
=(5-3/3)*100
=200/3 =
66.67%, option C