LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
22 views
in Aptitude by (30.0k points)
closed by
Rajdhani Express leaves Delhi for Dehradun. It crosses a Sandalwood tree in 9 seconds and a  KTM bike travelling in the same direction at 60 kmph in 90 seconds. Calculate the speed and the length of the train?
1. 300/9, 200/9
2. 200/7, 300/7
3. 300/7, 500/7
4. 200/3, 500/3

1 Answer

0 votes
by (41.6k points)
selected by
 
Best answer
Correct Answer - Option 4 : 200/3, 500/3

Given 

Time taken to cross a tree by train = 9 seconds

Speed of bike = 60 kmph

Time taken to cross the bike = 90 seconds

Formula Used 

Distance = Speed × Time

Calculation 

Case 1 ∶ Let the speed of the train be x km/hr or x × 5/18 m/sec

Time taken to cross a tree = 9 seconds

∴ Distance travelled = x × 5/18 × 9 = 5x/2 meter

So, length of the train = 5x/2 metres

Case 2 ∶ The speed of the bike = 60kmph

Relative speed of the train w.r.t bike = (x - 60) km/hr = (x - 60) × 5/18 m/sec

Time taken to cross the bike = 90 seconds

∴ Distance travelled = [(x - 60) × 5/18] × 90 = 25 (x - 60) meter

So, length of the train = 25 (x - 60) meter  

Solving above equations, we get

5x/2 = 25 (x - 60)

⇒ x = 10x - 600

⇒ 9x = 600

⇒ x = 600/9 = 200/3 km/hr

Hence distance travelled = 5x/2 = (5/2) × (200/3) = 500/3 meter

∴ The speed of the train is 200/3 km/hr and the length of the train is 500/3 meter.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...