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(#M40000896) TCS QUESTION colz and ink Keep an EYE

Alchemy is an occult tradition that arose in the ancient Persian empire. Zosimos of Panopolis was an early alchemist. Zara, reads about Zosimos and decides to try some experiments. One day, she collects two buckets, the first containing one litre of ink and the second containing one litre of cola. Suppose she takes one cup of ink out of the first bucket and pours it into the second bucket. After mixing she takes one cup of the mixture from the second bucket and pours it back into the first bucket. Which one of the following statements holds now?

a.There is more cola in the first bucket than ink in the second bucket.
b.There is as much cola in the first bucket as there is ink in the second bucket.
c.There is less cola in the first bucket than ink in the second bucket.

Solution

let the size of cup = x litre
then after first step
ink in first bucket = 1-x and ink in second = x in total 1+x amount of mixture
now we have to pour 1 cup means x litre of solution from second bucket to first
in this much of solution ink will be [x/(1+x)]*x] = x^2/(1+x)
so total ink in the first bucket = 1-x+[x^2/(1+x)]
so cola in first bucket = 1-[1-x+{x^2/(1+x)}] = x-[x^2/(1+x)]
similarly total ink in second bucket = x - amount of ink poured in first
= x - [x^2/(1+x)]
so cola in the first bucket = ink in the second bucket

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Asked In TCS Nirmal Bajpai (14 years ago)

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