Multiple choice

A container has a mixture of milk and water in the ratio 5:1. 12 litres of the mixture is taken out and replaced with water. Now the ratio of milk to water becomes 3:1. Find the original quantity of the mixture.

  1. 126 L

  2. 134 L

  3. 120 L

  4. 124 L

  5. 130 L
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial mixture be 6x (5x milk, 1x water). Removing 12L removes 10L milk and 2L water. Remaining: 5x-10 milk, x-2 water. Adding 12L water: 5x-10 milk, x-2+12 = x+10 water. Ratio (5x-10)/(x+10) = 3/1. 5x-10 = 3x+30. 2x = 40, x = 20. Total = 6x = 120L.

AI explanation

Let the original quantity of the mixture be V liters, where milk is 5V/6 and water is V/6. Using the formula for replacement, the remaining quantity of milk after replacing 12 liters with water is (5/6) multiplied by (V minus 12). Since the final total volume is V and the new ratio of milk to water is 3:1, the final volume of milk is 3V/4. Setting the expressions equal gives (5/6)(V - 12) = 3V/4, which simplifies to 10(V - 12) = 9V, meaning the original quantity of the mixture is 120 liters.

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