Infosys Sample Distance Calculation Questions

Question 1
A train starts from station P towards Q with certain speed. Due to a problem, after crossing 50km, the train slows down to 2/3 rd of its actual speed and it reaches Q 50 minutes later than the planned time. Suppose the technical problem had happened after crossing 60 km and the train would had reached 40 minutes late. What is the actual(original) speed of the train and what is the distance between P and Q ?
a)30km/hr, 100km b)20km/hr,80km c)40km/hr,150km d)50km/hr,150km
Answer : a)30km/hr, 100km
Solution:
Let the distance between P and Q be X and the speed initially be V.
Note that the train travels 50km with speed V and the remaining distance(X-50)km with speed 2/3 of V.
According to the above condition, with the formula " distance/speed = time", we can have
Time Taken For First 50 Km + Time Taken For Remaining (X-50) Km = Planned Time + Extra Time Due To Problem
[50/V]+[(X-50)/(2V/3)] = [X/V]+5/6 (here 50 minutes = 5/6 hours)
[100+3X-150-2X]/2V = 5/6
3X-5V = 150 ...eqn1
Suppose the technical problem had happened after crossing 60 km and the train would had reached 40 minutes late.
Using the same logic we used to arrive at eqn1, we get,
[60/V]+[(X-60)/(2V/3)] = [X/V]+2/3 (here 2/3 is for 40 minutes in hour.)
[120+3X-180-2X]/2V = 2/3
3X-4V = 180 ....eqn2
Solving eqn1 & eqn2, we get
X=100 & V=30
Hence the distance between P and Q is 100km and the actual speed of the train is 30km/hour.
Question 2
A train starts from A towards B with some velocity. Due to an engine problem, after travelling 3/8 of its journey, it slows to 3/5 of its actual velocity. The train reaches B 1 hour later than the actual planned time. If the engine had failed after travelling 80km and if it would had slowed down to 4/5th of its initial velocity for another 80km and covered remaining distance with 1/2 of its initial velocity, the train would had reached the destination one and half hours late. What is the distance between A and B in meters?
a)10000 b)48000 c)24000 d)52000
Answer : b)48000
Solution:
Let the distance between A and B be X and the speed initially be V.
The train travels 3X/8km with speed V and the remaining distance(X - 3X/8)km with speed 3/5 of V. Ultimately the train was late by 1 hour.
According to the above condition with the formula " distance/speed = time", we can have
[(3X/8)/V]+[(X-(3X/8))/(3V/5)] = [X/V]+1
[3X/8V] + 5(8X-3X)/24V = [X/V]+1
9X+25X-24X / 24V = 1
10X-24V = 0 ..........eqn1
According to the question, if the train travelled 80km with speed V, another 80km with 4/5 th of V and the remaining distance(X-160)km with speed 1/2 of V then
[80/V]+[80/(4V/5)]+[(X-160)/(1V/2)] = [X/V]+3/2
80/V + 100/V + (2X-360)/V = X/V + 3/2
X-180 / V = 3/2
2X-3V = 360 .........eqn2
solving eqn1 and eqn2
we have, X=480 and V=200
Thus the distance between A and B is 480km and the speed of the train is 200km/hour.
Hence 480km = 480000meters is the answer.
Question 3
A man rides a bike with speed V for a distance X km. After completing 1/2 of his journey he slows down to 1/2 of his initial speed and completes his ride half an hour late than planned time. What will be the ratio of the distance to the speed?
a)1:2 b)2:1 c)1:1 d)2:3
Answer : c)1:1
Solution:
Let the distance be X and the speed initially be V.
Using same logic as we used for previous two questions, we get,
X/2V + [X-(X/2)]/(V/2) = X/V + 1/2
X/2V + [4X-2X]/2V = X/V + 1/2
X/2V = 1/2
X = V or X/V = 1
Thus 1:1 is the required ratio.

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10th 3i InfoTech Academic Books Accenture ACIO ActiveX ADT Agricultural AIEEE Air Force Algebraic Amdocs Android Answers Application Development Aptitude Aptitude Questions Architectures ASP ATOS B.Sc B.Tech.B.E. Bank Exam BCA BE Board Exam Books break-continue Business Plan C C Programming C# C++ Campus campus interview Candidate profile Capgemini Career CDS Certification CET Challenge Circle Cisco class code Cognizant communication Company Company Profile Competitive Exams computer Computer Networks concentric circles constructor Course Credit Suisse CSS CTS Data Structure DBMS DC Deloitte difficult interview questions dimensions Distributed Computing do while dotNet Download ds Dynamic Web Development e-Admit card Educational engineering entertainment Even Odd Events exam schedule exception for loop fresher GATE general Discussion general knowledge Get Placed Government Job Hall Ticket HCL how to answer How to Prepare HR HR Interview HSC hypertext preprocessor IB IBM IBPS IIT Indian Army Information infosys Intelligence Bureau Internship interview Experience interview questions Interview Tips IntroC IntroC# IntroJava IntroPHP IT J2EE J2ME Java JavaScript jobs Language Books Language Tutorial Languages limit number of objectsJava Limit the number of objects being created in JAVA Linux Linux Administrator Linux Developer Logical Questions loops M Tech M.E. M.Tech M.Tech AND B.Tech Management Management Skills Matrices MBA mca ME microsoft mistakes Mixture Mobile Computing mock questions mock test MySql naukri NDA OOP opening Operating System Oracle paper Persistent PHP php programming php string variables PL/SQL Placement placement guide Placement Paper Placement Process preparing for placement presentation probability Problems Professional program Programming Project Engineer project idea Projects Puzzle qualities Question of the day Questions Quiz Question Recruitment Recruitment Pattern Requirement Result Resume Reviews Screen Sizes Scripting Session Skills Software Software Engineering solved papers Source Code Speed time and distance SQL SSC story Stress Interview Study Material study tips submit resume Synonym TCS Tech Mahindra tech news Technical Books Technical Interview Testing thank you letter Thought Time Table TutC++ Unix questions asked in aptitude and inteviews for MCA UPSC verbal Web Designing Web Developer Website Development What to read while loop Wipro Writing Resume