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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