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 400 m race, how much lead in terms of distance, can P give Q and still finish at the same time as Q?

- 43.4 m
- 56.6 m
- 32.1 m
- P cannot give a lead as Q is always ahead of P

32.1 m

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

Total distance in 48 sec = 312m

To cover balance 86 m with speed = 10 m/sec, time taken = 86/10 = 8.6 sec

So P would finish 400 m in 48 + 8.6 = 56.6 seconds.

In 56.6 seconds, Q cycles 56.6 * 6.5 = 367.9 m or B should have a 32.1 m 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?"**

Choice C is the correct answer.

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