CAT Exam Model Paper 4 with solutions for free online practice

Question : 29 of 60

Marks: +1, -0

From a solution that has milk and water in the ratio 5: 3, ‘x’percent is removed and replaced with water. The concentration of milk in the resulting soution lies between 30% and 50%. Which of the following best describes the value of 'x'?

25 < x < 50
20 < x < 52
20 < x < 48
25

Validate

Solution:

Let the quantity of total solution be 800 units.
So, quantity of milk is 500 units and water is 300 units.
Now x percent of 800 = 8x units mixture is removed.
The quantity (in units) of milk and water removed is 5x and 3x respectively.
Final concentration of milk (in percentage) is:

{ 500 - 5 x }/ { 800 } ×100

{ \So, } 30 < { 500 - 5 x } /{ 8 } < 50

⇒ 240 < 500 - 5 x < 400

⇒260 < - 5 x < - 100

⇒ 20 < x < 52

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