The question is from the topic Time and distance. This question tests our understanding of relationship between time and speed when the distance is constant. It is a classic question involving the concept of speed, distance and time. Time Speed and Distance is a favorite in CAT Exam, and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam.

Question 5: Mr. X decides to travel from Delhi to Gurgaon at a uniform speed and decides to reach Gurgaon after T hr. After 30 km, there is some engine malfunction and the speed of the car becomes \\frac{4}{5}\\)^{th} of the original speed. So, he travels the rest of the distance at a constant speed \\frac{4}{5}\\)^{th} of the original speed and reaches Gurgaon 45 minutes late. Had the same thing happened after he travelled 48 km, he would have reached only 36 minutes late. What is the distance between Delhi and Gurgaon?

- 90 km
- 120 km
- 20 km
- 40 km

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Let the distance from Delhi to Gurgaon be ‘d’ km.

The first 30 km he travels at his usual speed. However, the remaining ‘d-30’ km he travels at a reduced speed.

To travel ‘d’ km he usually takes T hr. Therefore, to travel ‘d - 30’ km he should ideally take \\frac{(d−30)T}{d}\\) hr. However, this is only if he travels at his usual speed. It is given that he traveled only at \\frac{4}{5}\\)^{th} of his usual speed. Because of this he would have taken \\frac{5}{4}\\)^{th} of the time to travel the remaining distance, i.e., he takes \\frac{1}{4}\\)^{th} of the time extra. This is given to be 45 minutes (or \\frac{3}{4}\\)^{th} hr)

\\frac{1}{4}\\)\\frac{(d−30)T}{d}\\) = \\frac{3}{4}\\) ........(1)

On the other hand, had the same thing happened after he travelled 48 km, he would have reached only 36 minutes or 34 hrs late. Hence,

\\frac{1}{4}\\)\\frac{(d−48)T}{d}\\) = \\frac{3}{5}\\) ........(2)

Dividing (1) by (2) and solving for d, we get d = 120 km.

The question is **What is the distance between Delhi and Gurgaon?** we get d = 120 km.

Choice B is the correct answer.

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