QUESTION

CSAT

Medium

Maths

Prelims 2025

A tram overtakes 2 persons X and Y walking at 3 km/h and 4 km/h in the same direction and completely passes them in 8 s and 9 s respectively. What is the length of the tram?

Select an option to attempt

Explanation

Let tram speed be aa km/h.

For both overtakes, the length (L) is the same: LL = (relative speed w.r.t. X) × 8 s = (relative speed w.r.t. Y) × 9 s

Relative speeds (in km/h): (a3)(a - 3) and (a4)(a - 4). The conversion to m/s cancels when equating: 8(a3)=9(a4)8a24=9a36a=128(a - 3) = 9(a - 4) \Rightarrow 8a - 24 = 9a - 36 \Rightarrow a = 12 km/h

Now compute LL using X: Relative speed = (123)=9(12 - 3) = 9 km/h = 9×(5/18)=2.59 \times (5/18) = 2.5 m/s L=2.5×8=20L = 2.5 \times 8 = 20 m

Trusted by 2L aspirants

Practice UPSC Prelims PYQs Smarter

Practice Now
  • Track accuracy & weak areas
  • See past trends & repeated themes
Start Practicing Now

Crack UPSC with your
Personal AI Mentor

An AI-powered ecosystem to learn, practice, and evaluate with discipline

SuperKalam is your personal mentor for UPSC preparation, guiding you at every step of the exam journey.

Download the App

Get it on Google PlayDownload on the App Store
Follow us

ⓒ Snapstack Technologies Private Limited