70 litres of a mixture of milk and water contains 20% water. How much water should be added so that the mixture has 28% water?a)50/9 litreb)60/9 litrec)70/9 litred)100/9 litree)None of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Let's solve the problem step by step:

Given information:
- 70 litres of a mixture of milk and water contains 20% water.

Step 1: Calculate the amount of water in the given mixture.
To find the amount of water in the mixture, we multiply the total volume of the mixture (70 litres) by the percentage of water (20%):
Amount of water = 70 litres × 20% = 70 × 0.20 = 14 litres

Step 2: Determine the desired concentration of water.
The problem states that we want the mixture to have a concentration of 28% water.

Step 3: Set up the equation.
Let's assume that x litres of water needs to be added to the mixture. The total volume of the mixture after adding water will be 70 + x litres. The amount of water in the new mixture will be 14 + x litres. We can set up the equation as follows:
(14 + x) / (70 + x) = 28%

Step 4: Solve the equation.
To solve the equation, we can cross-multiply:
(14 + x) × 100 = 28 × (70 + x)
1400 + 100x = 1960 + 28x

Next, we can simplify the equation:
100x - 28x = 1960 - 1400
72x = 560

Finally, we can solve for x by dividing both sides of the equation by 72:
x = 560 / 72
x ≈ 7.7778

Step 5: Round the answer.
Since we are dealing with a volume of liquid, it doesn't make sense to have a fractional part of a litre. Therefore, we should round the answer to the nearest whole number:
x ≈ 8 litres

Step 6: Choose the correct option.
Among the given options, the closest answer is 70/9 litres (≈ 7.7778 litres), which is option C.

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