# DBT JRF 2022 — Question 42

Exam: DBT JRF 2022 · Section: A · Topic: Aptitude › Speed, Distance & Time · Difficulty: Medium

## Question

A 100 m long train is running at a speed of 68 km/h. A man is also running in the same direction with a speed of 8 km/h. In what time will the train overtake the running man?

## Options

- **A.** 6 sec
- **B.** 9 sec
- **C.** 6 min
- **D.** 9 min

## Answer

Option A

## Explanation

Train overtaking a running man: Relative velocity of train with respect to the man (both moving in the same direction): $v_{\text{rel}} = 68 - 8 = 60\,\text{km/h}$ Convert to m/s: $60 \times \frac{1000}{3600} = \frac{60000}{3600} = \frac{50}{3}\,\text{m/s}$ The train must cover its own length (100 m) relative to the man to fully overtake him: $t = \frac{d}{v_{\text{rel}}} = \frac{100}{50/3} = 100 \times \frac{3}{50} = 6\,\text{seconds}$ Answer: 6 seconds (Option 1).

Source: https://mypyqbuddy.com/questions/a-100-m-long-train-is-running-at-6a104cd5920734408bc0c707