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There is a mixture of alcohol and water of 120 litres. The ratio of alcohol to water is 5 : 3. If 30% of the mixture is taken out and the same amount of water is added then find the new ratio of alcohol and water in the mixture.
- a)7:3
- b)5:8
- c)7:9
- d)11:4
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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There is a mixture of alcohol and water of 120 litres. The ratio of al...
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There is a mixture of alcohol and water of 120 litres. The ratio of al...
Given:
- Total mixture = 120 litres
- Ratio of alcohol to water = 5 : 3
To Find:
- New ratio of alcohol and water after 30% of the mixture is taken out and the same amount of water is added
Solution:
Let's assume the initial amount of alcohol and water in the mixture is 5x and 3x respectively.
So, the initial mixture can be represented as:
Alcohol = 5x litres
Water = 3x litres
Step 1: Calculate the initial amount of alcohol and water in litres:
Total mixture = Alcohol + Water
120 = 5x + 3x
120 = 8x
x = 15
So, the initial amount of alcohol = 5x = 5 * 15 = 75 litres
And the initial amount of water = 3x = 3 * 15 = 45 litres
Step 2: Calculate the amount of mixture taken out:
30% of the mixture is taken out, so the amount of mixture taken out = 30% of 120 litres = (30/100) * 120 = 36 litres
Step 3: Calculate the new amount of alcohol and water in the remaining mixture:
The amount of alcohol remaining = initial amount of alcohol - amount of alcohol taken out = 75 - 36 = 39 litres
The amount of water remaining = initial amount of water - amount of water taken out = 45 - 36 = 9 litres
Step 4: Calculate the amount of water added:
The same amount of water is added, which is equal to the amount of mixture taken out = 36 litres
Step 5: Calculate the new total mixture:
New total mixture = Remaining alcohol + Remaining water + Added water = 39 + 9 + 36 = 84 litres
Step 6: Calculate the new ratio of alcohol and water:
New ratio of alcohol to water = 39 : 9 = 13 : 3
Therefore, the new ratio of alcohol to water in the mixture is 13 : 3, which is equivalent to 7 : 9 (by dividing both the quantities by their common factor 13).
Hence, the correct answer is option C) 7:9.
- Total mixture = 120 litres
- Ratio of alcohol to water = 5 : 3
To Find:
- New ratio of alcohol and water after 30% of the mixture is taken out and the same amount of water is added
Solution:
Let's assume the initial amount of alcohol and water in the mixture is 5x and 3x respectively.
So, the initial mixture can be represented as:
Alcohol = 5x litres
Water = 3x litres
Step 1: Calculate the initial amount of alcohol and water in litres:
Total mixture = Alcohol + Water
120 = 5x + 3x
120 = 8x
x = 15
So, the initial amount of alcohol = 5x = 5 * 15 = 75 litres
And the initial amount of water = 3x = 3 * 15 = 45 litres
Step 2: Calculate the amount of mixture taken out:
30% of the mixture is taken out, so the amount of mixture taken out = 30% of 120 litres = (30/100) * 120 = 36 litres
Step 3: Calculate the new amount of alcohol and water in the remaining mixture:
The amount of alcohol remaining = initial amount of alcohol - amount of alcohol taken out = 75 - 36 = 39 litres
The amount of water remaining = initial amount of water - amount of water taken out = 45 - 36 = 9 litres
Step 4: Calculate the amount of water added:
The same amount of water is added, which is equal to the amount of mixture taken out = 36 litres
Step 5: Calculate the new total mixture:
New total mixture = Remaining alcohol + Remaining water + Added water = 39 + 9 + 36 = 84 litres
Step 6: Calculate the new ratio of alcohol and water:
New ratio of alcohol to water = 39 : 9 = 13 : 3
Therefore, the new ratio of alcohol to water in the mixture is 13 : 3, which is equivalent to 7 : 9 (by dividing both the quantities by their common factor 13).
Hence, the correct answer is option C) 7:9.
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