CAT Quantitative Aptitude Questions | CAT Time Speed and Distance & Races

CAT Questions | Speed Time | Relative speed
× CAT Questions
CAT Quantitative Aptitude
HCF and LCM Factors Remainders Factorials Digits Ratios,Mixtures;Averages Percents; Profits; SICI Logarithms and Exponents Pipes,Cisterns; Work,Time Set Theory Geometry Coordinate Geometry Mensuration Trigonometry Linear & Quadratic Equations Functions Inequalities Polynomials Progressions Permutation Probability
CAT Verbal
Para Jumble Sentence Correction Sentence Elimination Paragraph Completion Reading Comprehension Critical Reasoning Word Usage Para Summary Text Completion
CAT LR DI
DI LR: Bar Graphs DI LR: Pie Charts DI LR: Multiple Graphs DI LR: Word Problems DI LR: Line Graphs DI LR: Sequencing DI LR: Grid Puzzles DI LR: Math Puzzles DI LR: Visualization DI LR: Other Patterns DI LR: CAT 2017 Cet DI LR: CAT 2017 Rural Survey DI LR: CAT 2017 Happiness DI LR: CAT 2017 Airlines DI LR: CAT 2017 Travel Route DI LR: CAT 2017 Food Delivery DI LR: CAT 2017 Square Layout DI LR: CAT 2017 Team Project DI LR: CAT 2017 Assets DI LR: CAT 2017 Pizza DI LR: CAT 2017 Electives DI LR: CAT 2017 Chess DI LR: CAT 2017 Dorms DI LR: CAT 2017 Tea DI LR: CAT 2017 Friends DI LR: CAT 2017 Security Scan
CAT Online Coaching
CAT Question MenuCAT Questions

The question is from the topic relative Speed. This is relatively a straightforward question and only tests the basic concepts. Time Speed and Distance is a favorite in CAT Exam and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 25: Two persons A and B start moving from point P towards Q which are 1400 Km apart. Speed of A is 50 Km/hr and that of B is 20 Km/hr. How far is A from Q when he meets B for the 22nd time?

  1. 1000 Km
  2. 600 Km
  3. 800 Km
  4. 1400 Km

🎯 Huge Discount: 3,500 off on Online CAT Course. Till June 1. Register now!


2IIM : Best Online CAT Coaching.


Best CAT Coaching in Chennai


CAT Coaching in Chennai - CAT 2020
Online Batches Available Now!


Explanatory Answer

Method of solving this CAT Question from Time Speed Distance:

Let's consider the Distance between P and Q, which is 1400km as one lap.
The Speeds of A and B are in the ratio 5 : 2. That means by the time A coimpletes 5 laps, B completes just 2 laps.

Both of them start moving from P, so after 5 laps(odd number of laps) A will be at Q, and B will be at P(even number of laps).
Seeing it from the perspective of A, he would have met P once evevy lap that he has made except the first lap since they are moving in the same dirction in the first lap.
So A and B would have met 5-1=4 times.

Let's consider another round of 5 laps. A runs 5 more laps and B runs 2 more laps
This time A starts from Q and after 5 laps reaches P, while in the same time B starts from P and ends at P.
This time they would have met exactly 5 times

Consolidating everything, we can say that A runs 10 rounds and B runs 4 rounds in the same time, reaching their original positions, meeting each other exactly 9 times

So cyclicity kicks in here....

22 can be written as 9 + 9 + 4.

After every 9 meets, A and B reach their original positions, that is both of them are at P. So, after 18 meets they both remain at P, For 4 more meets A must take 5 laps and B 2 laps, A being at Q and B at P at the end.

So at the end of this, A is at Q and B is at P.

Which means their last meet happened while they were travelling away from each other, which implies that they in the process together covered one lap(1400 km) after the last meet.
Which mean sA covered 5/7 th of 1400km after the last meet, ehich is the same as the distance between the last meeting point and Q.

So distance A and Q when he meets B for the 22nd time = 5/7 th of 1400km = 1000km

The question is " How far is A from Q when he meets B for the 22nd time? "

Hence, the answer is 1000 Km

Choice A is the correct answer.

 


CAT Preparation Online | CAT Arithmetic Videos On YouTube


Other useful sources for Arithmetic Question | Time Speed Distance and Races Sample Questions


CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com