Aryan runs at a speed on 40 metre/ minute. Rahul follows him after an interval of 5 minutes and runs at a speed of 50 metre/minute. Rahuls dog runs at a speed of 60 metre/minute and starts along with Rahul. The dog reaches Aryan and then comes back to Rah

examrobotsa's picture

Submitted by examrobotsa on

Q: 68 (IAS/2005)
Aryan runs at a speed on 40 metre/ minute. Rahul follows him after an interval of 5 minutes and runs at a speed of 50 metre/minute. Rahul’s dog runs at a speed of 60 metre/minute and starts along with Rahul. The dog reaches Aryan and then comes back to Rahul, and continues to do so till Rahul reaches Aryan. What is the total distance covered by the dog?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,3,5,1,2,2,3

keywords: 

{'total distance': [0, 0, 1, 0], 'metres': [0, 1, 1, 0], 'rahul': [0, 0, 6, 0], 'minutes': [0, 0, 1, 1], 'dog': [4, 0, 3, 1], 'speed': [0, 1, 2, 0], 'minute': [0, 0, 1, 0], 'aryan': [0, 0, 5, 1], 'metre': [0, 3, 4, 3], 'interval': [2, 0, 2, 4]}

In this problem, we are calculating the total distance covered by Rahul`s dog.

Option 1: This can`t be the correct answer because even if the dog only ran at Aryan`s pace (40 metres/minute), it would cover 600 metres in 15 minutes. But we know the dog runs faster, so the distance it covers must be greater than 600 metres.

Option 2: This can`t be the correct answer too since we have established that the distance the dog covers is more than 600 metres.

Option 3: This still doesn`t suffice because the dog is running at a speed of 60 metres/minute. So in 15 minutes, it would cover at least 900 metres (15 * 60), without taking into account its return trips to Rahul.

Option 4 : 1200 meters is the correct answer. The reasoning is that Aryan had a five-minute head start, so he travelled 200 metres before Rahul and the dog started. It would take Rahul (who runs at 50 metres per minute) 20 minutes to catch up to Aryan. Since the dog runs at 60 metres per minute, in those 20 minutes, the dog would have covered 1200 metres (20 * 60).