83 Views

Question : Train A running at 81 km/hr takes 72 sec to overtake train B, when both the trains are running in the same direction, but it takes 36 sec to cross each other if the trains are running in the opposite direction. If the length of train B is 600 metres, then find the length of train A (in metres).

Option 1: 600

Option 2: 480

Option 3: 590

Option 4: 900


Team Careers360 5th Jan, 2024
Answer (1)
Team Careers360 11th Jan, 2024

Correct Answer: 480


Solution : Let the length of train A be $L{_A}$ and the speed of train B be $S{_B}$ km/hr.
When both trains are running in the same direction,
Distance = relative speed $\times$ time
⇒ $L{_A}+600 = (81-S{_B})\times\frac{5}{18}\times 72$
⇒ $L{_A}+600 = (81-S{_B})\times 20$
⇒ $L{_A}+20S{_B} = 1020$ ........(1)
When both the trains are running in the opposite direction,
⇒ $L{_A}+600 = (81+S{_B})\times\frac{5}{18}\times 36$
⇒ $L{_A}+600 = (81+S{_B})\times 10$
⇒ $L{_A}-10S{_B} = 210$
Multiplying by 2 we get,
⇒ $2L{_A} - 20S{_B} = 420$
⇒ $20S{_B} = 2L{_A} -420$........(2)
Now, putting the value from equation (2) in (1), we get,
⇒ $L{_A} + 20S{_B} = 1020$
⇒ $L{_A} + 2L{_A} - 420 = 1020$
⇒ $3L{_A} = 1440$
⇒ $L{_A} = 480\ \mathrm{m}$
Hence, the correct answer is 480.

SSC CGL Complete Guide

Candidates can download this ebook to know all about SSC CGL.

Download EBook

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books