A Train Starts from Agra to Mathura at 60 km/h and Reaches There in 45 min GMAT Problem Solving

Question: A train starts from Agra to Mathura at 60 km/h and reaches there in 45 min. If at the time of returning its speed is reduced by 10%, how much time will it take from Mathura to Agra?

  1. 45 min
  2. 50 min
  3. 1 hour
  4. 1 hour 20 min
  5. 1 hour 20 min

Correct Answer: B

Solution and Explanation:
Approach Solution 1:

For Agra to Mathura, the initial train speed=60 km/hr
The train reaches Agra to Mathura in 45 min
Hence, we get 45/60 hr
The distance between Agra to Mathura = 60*45/60 km =45 km

Now, for the second part of the question.
The speed is reduced by 10% at the time of return.
Hence, the reduced speed of the train = 60 - (10% of 60) km/hr = 60 - 6 = 54 km/hr

Therefore, the time taken in the return journey = Distance travelled/reduced speed
We already know from the first part that the distance is 45 kilometres.
=45/54 km/hr
=(5/6)
Now to convert this into time, we multiply by 60 minutes.
(5/6) *60 min
=50 min

Approach Solution 2:
The distance between Agra and Mathura is 60 x 45/60 = 45 km.
Since the returning speed is reduced by 10%
60 x 0.9 = 54 km/h,
The time it takes to return to Agra from Mathura = 45/54 (since from the first part, we know that the distance is 45 kilometres)
= 5/6 hr
=\(\frac{5}{6}\)*60
= 50 minutes.

Approach Solution 3:
Let the distance between Agra and Mathura be s.

The speed of the train as given in the question is 60 km/hr
The time taken by the train to cover the distance s with a constant speed of 60 km/hr is 45 mins.
Now, we need to convert the time into hours since the speed is in km per hour.
To convert time into hours, we must divide the time in minutes by 60.
⇒ 45/60 = 3/4= 0.75
Therefore, the time is 0.75 hours.

Now, we need to find the distance between Agra and Mathura by applying the speed formula (speed=distance/time).
⇒60 = s/0.75
⇒s= 60 * 0.75
⇒s= 45
Therefore, the distance between Agra and Mathura is 45 km.
Given that, on the return journey, the speed is reduced by 10%.
Therefore, the modified speed will be (original speed – 10% of original speed).
10% of the original speed is 10/100 × 60 = 6
Therefore, the modified speed will be (60 – 6) = 54 km/hr.

Now, we need to find the time t required to cover 45 km of distance at a speed of 54 km/hr by using the speed formula.  
⇒54=45/t
⇒t=45/54
⇒t=0.83

Therefore, the time required to cover this distance is 0.83 hours.

Now, it is required to convert this time into mins.

To convert from hours to mins, we have to multiply the time by 60.
Time in mins = 0.83×60=50 mins.

“A train starts from Agra to Mathura at 60 km/h and reaches there in 45 min”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. The GMAT Quantitative reasoning section tests the analytical and calculative skills of the candidates. The candidates must solve more GMAT Problem Solving questions like this to enhance their skills in cracking numerical problems. GMAT Quant practice papers will further help the candidates to analyse various questions that will enable them to score better marks in exams.

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