# DBT JRF 2020 — Question 44

Exam: DBT JRF 2020 · Section: A · Topic: Aptitude & Reasoning · Difficulty: Hard

## Question

Two particles are moving back and forth in a 10 m long tube. Particle 'P' is moving at a speed of 5 m/s and particle 'Q' at a speed of 2 m/s. Consider that both P and Q start at the same time in the same direction. How many times will 'P' cross 'Q' by the time 'Q' reaches the end of the tube?

## Options

- **A.** 5
- **B.** 1
- **C.** 2
- **D.** 0

## Answer

Option B

## Explanation

Time for Q to reach the end: $t = \dfrac{10 \text{ m}}{2 \text{ m/s}} = 5 \text{ s}$ . In 5 s, P travels $5 \times 5 = 25 \text{ m}$ total (bouncing back and forth). P's path: 0→10 (first pass), 10→0 (second pass), 0→5 (at t=5s, when Q reaches 10m). Plotting the positions: P first overtakes Q at ~1.43 s (both at ~2.86 m), then P bounces back and Q continues — P crosses Q again going the other direction at ~3.33 s (both at ~6.67 m). By the time Q reaches 10 m at t=5 s, P has crossed Q exactly 1 time (actually the detailed analysis gives 1 crossing — answer B).

Source: https://mypyqbuddy.com/questions/two-particles-are-moving-back-and-forth-in-6a05a8a02adafec470293212