BTGModeratorVI wrote: ↑Wed Dec 16, 2020 12:45 pm
Excluding stoppages, the speed of a bus is 54km/hr and including stoppage, it is 45km/hr. For how many minutes does the bus stop per hour?
(A) 9
(B) 10
(C) 12
(D) 15
(E) 20
Answer:
B
Solution:
Let the total distance the bus travels be d. Let the bus travel for t hours in total and stop for s hours in total. Notice that the speed of the bus is d/t excluding stoppage and d/(t + s) including stoppage. Setting the first expression equal to 54, we obtain:
d/t = 54
Similarly, setting the second expression equal to 45, we obtain:
d/(t + s) = 45
Let’s rewrite the first equation as d = 54t and substitute this expression for d in the second equation:
54t/(t + s) = 45
54t = 45(t + s)
54t = 45t + 45s
9t = 45s
t = 5s
Now, notice that the ratio of the time the bus stops to the total travel time is s/(t + s). Substituting t = 5s, we see that the bus spends s/(5s + s) = s/6s = 1/6 of every hour stopping, which is equivalent to 60 * 1/6 = 10 minutes of stopping each hour.
Answer: B
