Question
A boss decides to distribute Rs. 2000 between 2 employees. He knows X deserves more that Y, but does not know how much more. So he decides to arbitrarily break Rs. 2000 into two parts and give X the bigger part. What is the chance that X gets twice as much as Y or more?
CAT 2021
Solution
Correct option is
(D)
Explanatory Answer :
The bigger part could be any number from 1000 to 2000.
Now, if the bigger part is to be at least twice as much as the smaller part, we have
X ≥ 2Y or X ≥ 2(2000 – X)
Or X ≥ 4000/3
Given that X lies between 1000 and 2000, then the the probability that X lies between 4000/3 and 2000
This probability is equal to 2000−(4000/3)/2000−1000 = 2/3
Hence the answer is "2/3"
