Question

The ratio of milk and water is 10: 7 in a solution. If ‘x’ percentage is removed and replaced with water. The concentration of milk in the resulting solution lies between 30% and 50%. Then, which of the following best describes the value of ‘x’?

1. 15< x < 49
2.

20< x< 52

3.

21< x < 34

4. 25< x < 60

Answer 1

Correct Answer - Option 1 : 15< x < 49

Let the quantity of the total solution be 1700 units.

So, the quantity of milk is 1000 units and water is 700 units.

Now, x percent of 1000 = 10x unit mixture is removed.

The quantity (in units) of milk and water removed is 10x and 7x respectively.

Final Concentration of Milk (in %) is:

[(1000 – 10x)/1700] × 100 = (1000 – 10x)/17

So, 30< (1000 – 10x)/17 < 50

⇒ 510 < (1000 – 10x) < 850

⇒ -490< -10x < - 150

⇒ 150< 10x< 490

⇒ 15< x< 49