A takes 2 hours more than B to cover a distance of 40 km. If A doubles his speed, he takes 1½ hours more than B to cover 80 km. To cover a distance of 90 km, how much time will B take travelling at his same speed?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 1
Concept
We will use the concept of inverse relationshion between Speed and Time.
Application
Let the speed of B be x kmph
Time taken by B to cover 40 km = 40/x
Since A takes 2 hours more than "B"
Time taken by A = (40/x) + 2
The speed of A = (20x)/(20 + x)
According to the question
Distance = 80 km
Time taken by B to cover 80 km = 80/x ----(2)
When A doubles his speed = (40x)/(20 + x)
Total Time taken by A to cover 80 km = (40 + 2x)/(x) ----(3)
A.T.Q., A takes 3/2 hours more than B
(80/x) + (3/2) = (40 + 2x)/x
Upon solving
2 (40 + 2x - 80) = 3x
2 (2x - 40) = 3x
4x - 80 = 3x
4x - 3x = 80
x = 80
Actual Speed of B = 80 kmph
Distance To Be Covered By B = 90 km
Total Time taken by B = 90/80 = 1hours