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A mixture of 40 litres of milk and water contains 10% water. How much water must be added to make water 20% in the new mixture?
- a)10 litres
- b)7 litres
- c)5 litres
- d)3 litres
Correct answer is option ''. Can you explain this answer?
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A mixture of 40 litres of milk and water contains 10% water. How much...
Milk = 90/100 × 40 = 36 litres
View all questions of this test
water = 5 litres
∴ 5x + 20 = 40 + x
x = 5
Most Upvoted Answer
A mixture of 40 litres of milk and water contains 10% water. How much...
Understanding the Initial Mixture
In a 40-liter mixture of milk and water, where water constitutes 10% of the mixture:
- Water content: 10% of 40 liters = 4 liters
- Milk content: 40 liters - 4 liters = 36 liters
Setting Up the New Mixture
We want to add water to this mixture to make the new composition 20% water. Let’s denote the amount of water to be added as 'x' liters.
After adding 'x' liters of water, the total volume of the mixture becomes:
- New total volume = 40 liters + x liters
The new amount of water in the mixture will then be:
- New water content = 4 liters + x liters
Calculating the New Percentage
We want the new mixture to have 20% water:
- Equation: (4 + x) / (40 + x) = 20%
To eliminate the fraction, we can cross-multiply:
- Cross-multiplying: 4 + x = 0.2 * (40 + x)
This simplifies to:
- 4 + x = 8 + 0.2x
Rearranging gives us:
- 0.8x = 4
- x = 4 / 0.8
- x = 5 liters
Conclusion
To achieve a mixture where water constitutes 20%, you need to add 5 liters of water. Thus, the correct answer is option 'C' (5 liters).
In a 40-liter mixture of milk and water, where water constitutes 10% of the mixture:
- Water content: 10% of 40 liters = 4 liters
- Milk content: 40 liters - 4 liters = 36 liters
Setting Up the New Mixture
We want to add water to this mixture to make the new composition 20% water. Let’s denote the amount of water to be added as 'x' liters.
After adding 'x' liters of water, the total volume of the mixture becomes:
- New total volume = 40 liters + x liters
The new amount of water in the mixture will then be:
- New water content = 4 liters + x liters
Calculating the New Percentage
We want the new mixture to have 20% water:
- Equation: (4 + x) / (40 + x) = 20%
To eliminate the fraction, we can cross-multiply:
- Cross-multiplying: 4 + x = 0.2 * (40 + x)
This simplifies to:
- 4 + x = 8 + 0.2x
Rearranging gives us:
- 0.8x = 4
- x = 4 / 0.8
- x = 5 liters
Conclusion
To achieve a mixture where water constitutes 20%, you need to add 5 liters of water. Thus, the correct answer is option 'C' (5 liters).
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A mixture of 40 litres of milk and water contains 10% water. How much water must be added to make water 20% in the new mixture?a)10 litresb)7 litresc)5 litresd)3 litresCorrect answer is option ''. Can you explain this answer?
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