A Train can Travel 50% Faster than a Car GMAT Problem Solving

Qusetion: A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:

1. 100 kmph
2. 110 kmph
3. 120 kmph
4. 130 kmph
5. 230 kmph 

‘A train can travel 50% faster than a car’ – is a part of GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "Manhattan Prep's "GMAT Foundations of Math, 5th Edition"" published in the year 2007. GMAT Quant section consists a total of 31 questions. This is a GMAT Problem Solving question that allows the candidates to select the correct answer from the five answer choices provided. The total time allotted for this part is 62 minutes which allows the candidate 2 minutes to answer each question.

Solution and Explanation:

Approach Solution 1

There is only one approach to solve the problem statement.

Given: 

• A train can travel 50% faster than a car. 
• Both start from point A at the same time 
• They reach point B 75 kms away from A at the same time. 

Condition:

• On the way, however, the train lost about 12.5 minutes while stopping at the stations. 

Find Out: 

• The speed of the car

Let us consider that the speed of car is v

As per the question, the speed of train is 50% more than the car = 1.5 * v
Distance traveled by both of them is 75km each.
Since both start at the same time and reach at the same time so time taken by both of them will be same.
Time take by Car = time taken by train
Now, if we put this in equation, we get:

75/v = 75/1.5v + 12.5 (as train stopped in between for 12.5mins) (calculating speed in km/min)

75/v - 75/1.5v = 12.5
75/v ( 1 - 1/1.5) = 12.5
75/v ( (1.5-1)/1.5) = 12.5
75/v * 0.5/1.5 = 12.5
75/v = 12.5 * 1.5/0.5
75/v = 12.5*3 = 37.5
v = 75/37.5 
= 2 km/min
= 2*60 km/hr (as 1min = 1/60 hr)
= 120 km/hr

Hence, the correct answer is C. 

Correct Answer: C

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