Narenn wrote:

A Nice Question from VERITAS.

OA and OE will be posted after few responses. Brief and Correct explanations will be rewarded with a Kudo.John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.

A) 25%

B) 50%

C) 75%

D) 100%

E) 200%

Happy Solving!

Took some time to understand the Q.

Here is my Solution.

Let distance be John and Karen by 90 Kms

John's speed: 10 km/hr ---Time taken: 9 hrs

Karen's speed: 15Km/hr, time taken : 6 hrs

Now if both are running at their constant speed then they will meet in 3 hrs 36 minutes (See below)

at 0 hrs ---Distance between the 2 is 90 kms

after 1 hrs: 65 Km

After 2 hrs : 40 kms

After 3 : 15 kms

In 1 hr distance covered by the 2 jointly is 25 kms so 15 kms will be covered in 15/25*60----> 36 minutes

At the meeting point Distance covered by John : 36 Kms and by Karen: 54 Kms

Now John covered on D/4 distance ie. 22.5 Km distance and thus Karen would have to travel the extra distance of 13.5 kms.

To cover 13.5 kms----> Karen would need 54 mins (13.5/15*60---- 54 minutes)

So Total time taken by Karen : 3 hrs 36 minutes+ 54 minutes----> 4.5 hrs or 9/2 hrs

Usual time: 3hr 36 minutes -----> 18/5 hrs

Hence % More ((9/2-18/5) / 18/5 )*100-----> 25%

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