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Question

Sohan covers a total distance of 760 km to reach his home, traveling partly by train and partly by car. He takes 8 hours when he travels 160 km by train and the rest by car. If he travels 240 km by train and the remaining distance by car, his journey takes 12 minutes longer. Find the difference between the speeds of the train and the car.

This question was previously asked in
RRB ALP 2025 CBT 2 Wiremen Question Paper (28-Jul-2026) (Shift 2)
The correct answer is

20 km/h

To solve this problem, we are given two scenarios where Sohan travels a total distance of 760 km partly by train and partly by car. We need to find the difference in speeds between the train and the car.

  1. In the first scenario, Sohan covers 160 km by train and the remaining 600 km (760 km - 160 km) by car in 8 hours.
  2. Let the speed of the train be \(T\) km/h and the speed of the car be \(C\) km/h.
  3. The time taken to travel by train is \(\frac{160}{T}\) hours, and by car is \(\frac{600}{C}\) hours. Therefore, we can write the equation: \(\frac{160}{T} + \frac{600}{C} = 8\)
  4. In the second scenario, Sohan travels 240 km by train and 520 km by car, taking 12 minutes longer. In terms of hours, this converts to \(\frac{12}{60} = \frac{1}{5}\) hours.
  5. The equation for the second scenario is: \(\frac{240}{T} + \frac{520}{C} = 8 + \frac{1}{5}\)
  6. Simplifying the second equation, we have: \(\frac{240}{T} + \frac{520}{C} = \frac{41}{5}\)
  7. Now, let's solve these two simultaneous equations:
    • Equation 1: \(\frac{160}{T} + \frac{600}{C} = 8\)
    • Equation 2: \(\frac{240}{T} + \frac{520}{C} = \frac{41}{5}\)
  8. Multiply the entire first equation by 5 to eliminate the fraction: \(5 \cdot \left(\frac{160}{T}\right) + 5 \cdot \left(\frac{600}{C}\right) = 40\)
  9. Equation becomes: \(\frac{800}{T} + \frac{3000}{C} = 40\)
  10. Multiply the entire second equation by 5: \(5 \cdot \left(\frac{240}{T}\right) + 5 \cdot \left(\frac{520}{C}\right) = 41\)
  11. Equation becomes: \(\frac{1200}{T} + \frac{2600}{C} = 41\)
  12. Solving these simplified equations using substitution or elimination method, we derive: \(C - T = 20\)
  13. Therefore, the difference in speeds between the car and the train is 20 km/h.

Hence, the correct answer is 20 km/h.

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Similar Questions

  1. Krishna cycled a distance of 90 km at a certain speed. If he cycled 3 km/h slower, he would have taken 5 more hours to reach his destination. What is the speed in km/hr at which Krishna actually cycled?

  2. A man misses a train by 1 hour if he travels at a speed of 4 kmph, if he had increased his speed to 5 kmph, he would have still missed the train by 24 minutes. At what speed should he have travelled so that he reached the station exactly on time?

  3. A cyclist covers 500 m in 5 minutes. What distance (in km) would the cyclist cover in half an hour if he travels at the same speed?

  4. Travelling at 4/5 th of his usual speed, a man is 15 minutes late. What is his usual time to cover the same distance?

  5. The distance between two places can be covered in \(3\frac{1}{2}\) hours at a speed of 62 km/hr. If the speed is increased by 8 km/hr, how much time would be saved?


Important Questions from Partial Speed

  1. A train having length 210 metres takes 25 seconds to cross a 540 metres long bridge. How much time will the train take to cross a 630 metres long bridge?

  2. A person X from a place A and another person Y from a place B set out at the same time to walk towards each other. The places are separated by a distance of 15 km. X walks with a uniform speed of 1.5 km / hr and Y walks with a uniform speed of 1 km / hr in the first hour, with a uniform speed of 1.25 km / hr in the second hour and with a uniform speed of 1.5 km / hr in the third hour and so on.

    Which of the following is / are correct?

    1. They take 5 hours to meet.

    2. They meet midway between A and B.

    Select the correct answer using the code given below:

  3. The speed of a train is 120 kmph. What is the distance covered by it in 15 minutes?

  4. I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways ?

  5. Karan had covered two third of a certain distance when his car had a breakdown. He parked it and covered the remaining distance on foot. His time of travel on foot was 9 times his time of travel on car. What is the ratio of his walking speed with respect to his car’s speed?

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