Multiple choice

A container contains V litres solution of milk and water in the ratio 3 : 2. If 10 litres of water is added and the concentration of milk in the resultant solution lies between 50% and 40%, find the range of values of V.

  1. 50 < V < 60

  2. 20 < V < 50

  3. 30 < V < 40

  4. Insufficient data

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial milk is 0.6V, water is 0.4V. After adding 10L water, total volume is V+10. Milk concentration is 0.6V / (V+10). Setting 0.4 < 0.6V/(V+10) < 0.5 leads to 0.4V + 4 < 0.6V < 0.5V + 5. Solving 0.4V + 4 < 0.6V gives V > 20. Solving 0.6V < 0.5V + 5 gives V < 50.

AI explanation

Let the initial volume be V, meaning it contains 3V/5 L of milk. Adding 10 L of water makes the total volume V + 10 L. The concentration of milk becomes (3V/5) / (V + 10), which must lie strictly between 0.40 and 0.50. Solving (3V/5) / (V + 10) > 0.4 yields V > 20, and solving (3V/5) / (V + 10) < 0.5 yields V < 50, giving the range 20 < V < 50.

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