Excluding Stoppages, The Speed of a Bus is 54km/hr and Including Stoppage GMAT Problem Solving

Question: 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

Correct Answer: B

Solution and Explanation
Approach Solution 1:
This above-given problem can be solved using distance, time and speed formulas. Let us consider that the average speed (including stoppage) is 45 km per hour. Hence, Distance becomes rate* time.

So, in ONE hour, the distance traveled equals 45*1 = 45 km.
The average speed (excluding stoppage) is 54 km/hr
At this speed, the time required by bus to travel 45 km:
time = distance/rate
So, time = 45/54
= 5/6 hours
= 50 minutes
At a speed of 54 km/hr, the bus can travel 45 km every 50 minutes.
So, it must be motionless for the other 10 minutes.

Approach Solution 2:
We are given that the speed of the Bus with stoppage is 45km/hr. This means the Bus actually travels 45 km in an hour. This does not mean the bus actually traveled for 60 minutes, because it is given that the bus had stoppages. Now the duration of the hour the bus actually travels, the speed of the bus during that duration is 54km/hr.
So let's consider that the bus actually travels for T minutes in an hour. From the given information we can say:
54 * T/60 = 45
T = 45 *60/54 = 50 minutes.

The duration of the stoppage is 1 hour which makes (60 - 50) = 10 mins. So for 10 minutes the bus stops per hour.

Approach Solution 3:
L.C.M. of 54 and 45 = 270
Therefore, time taken by bus to cover 270 km excluding stoppages =54270​= 5hours

Time taken by bus to cover 270 km including stoppages = 45270​= 6hours

Theredore, the time for which the bus stops per hour =66−5​hours= 61​×60min= 10min.

“Excluding stoppages, the speed of a bus is 54km/hr and including stoppage”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide 2018 Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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