CAT 2015 Quantitative Ability

Question : 4 of 34

Marks: +1, -0

From a vessel completely filled up with pure wine,140 litres of content is removed and replaced with equal quantity of water. The process is repeated one more time. In a 98 litres sample of the resulting solution 80 litres is water. Find the capacity (in litres) of the vessel.

Your Answer:

Validate

Solution:

Let x be the initial quantity of wine in the vessel, y litres of content is removed twice. The part of wine left is

x(1-\;\;{y}/{x})^{2}

Now in 98 L of sample 18 L is wine which is same as

18/98

part of the solution

(1-\;\;{y}/{x})^{2}=\;\;{(x-y)^{2}}/{x^{2}}=\;\;{18}/{98}=\;\;{9}/{49}

⇒\;\;{(x-140)^{2}}/{x^{2}}=\;\;{9}/{49}⇒x=245

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