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

CAT Questions

The question is from the topic races. One cycles at a constant speed and other increases his speed for every 8 seconds. 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 14: P cycles at a speed of 4 m/s for the first 8 seconds, 5 m/s for the next 8 seconds, 6 m/s for the next 8 and so on. Q cycles at a constant speed of 6.5 m/s throughout. If P and Q had to cycle for a 436 m race, how much lead in terms of distance, can P give Q and still finish at the same time as Q?

1. 43.4 m
2. 56.6 m
3. 46 m
4. P cannot give a lead as Q is always ahead of P

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Explanatory Answer

Method of solving this CAT Question from Races: Speed * time = distance, this is enough to solve this question.

Distance covered by P in 8 sec = 4 * 8 = 32 m
Distance covered by P in 16 sec = 32 + 5 * 8 = 72 m
Distance covered by P in 24 sec = 72 + 6 * 8 = 120 m
Distance covered by P in 32 sec = 120 + 7 * 8 = 176 m
Distance covered by P in 40 sec = 176 + 8 * 8 = 240 m
Distance covered by P in 48 sec = 240 + 9 * 8 = 312 m
Distance covered by P in 56 sec = 312 + 10 * 8 = 392 m
Total distance in 56 sec = 392m
To cover balance 436 - 392 = 44 m with speed = 11 m/sec, time taken = 44/11 = 4 sec
So P would finish 436 m in 56 + 4 = 60 seconds.

In 60 seconds, Q cycles 60 * 6.5 = 390 m or B should have a 436 - 390 = 46m lead to result in a dead heat.

The question is "If P and Q had to cycle for a 400 m race, how much lead in terms of distance, can P give Q and still finish at the same time as Q?"

Hence, the answer is 46 m

Choice C is the correct answer.