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There are three vessels each of 20 litre capacity is filled with the mixture of milk and water. The ratio of milk and water are 2:3, 3:4 and 4:5 respectively. All the vessels are emptied into fourth vessel, then find the ratio of milk and water in the final mixture.
- a)401/543
- b)401/544
- c)401/545
- d)401/546
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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There are three vessels each of 20 litre capacity is filled with the m...
Answer – b) 401/544 Explanation : Milk = 2/5 + 3/7 + 4/9 and water = 3/5 + 4/7 + 5/9 so ratio will be 401/544
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There are three vessels each of 20 litre capacity is filled with the m...
Problem Analysis:
We are given three vessels of 20 litres capacity each filled with a mixture of milk and water in different ratios. We need to find the ratio of milk and water in the final mixture when all the three vessels are emptied into a fourth vessel.
Given:
- Three vessels of 20 litres capacity filled with mixtures of milk and water in the ratios of 2:3, 3:4, and 4:5 respectively.
To find:
- The ratio of milk and water in the final mixture when all the three vessels are emptied into a fourth vessel.
Solution:
Let us assume that the amount of milk and water in each vessel is proportional to the given ratios. Therefore, we can write:
- First vessel: Milk = 2x litres and Water = 3x litres
- Second vessel: Milk = 3y litres and Water = 4y litres
- Third vessel: Milk = 4z litres and Water = 5z litres
Now, when all the three vessels are emptied into a fourth vessel, the total amount of milk and water in the fourth vessel will be:
- Milk = 2x + 3y + 4z litres
- Water = 3x + 4y + 5z litres
We know that the total capacity of the fourth vessel is 60 litres (20 litres x 3 vessels). Therefore, we can write:
- Milk + Water = 60
- 2x + 3y + 4z + 3x + 4y + 5z = 60
- 5x + 7y + 9z = 60
Now, we need to find the ratio of milk and water in the final mixture. Therefore, we can write:
- Milk : Water = (2x + 3y + 4z) : (3x + 4y + 5z)
- Milk : Water = (2x + 3y + 4z) / (3x + 4y + 5z) : 1
Substituting the value of (5x + 7y + 9z) = 60, we get:
- Milk : Water = (2x + 3y + 4z) / (3x + 4y + 5z) : 1
- Milk : Water = (2x + 3y + 4z) / (5x + 7y + 9z - 2x - 3y - 4z) : 1
- Milk : Water = (2x + 3y + 4z) / (3x + 4y + 5z) : (5x + 7y + 9z - 2x - 3y - 4z) / (3x + 4y + 5z)
- Milk : Water = (2x + 3y + 4z) / (3x + 4y + 5z) : (3x + 3y + 4z) / (3x + 4y + 5z)
- Milk : Water = 2x + 3y + 4z : 3x + 3y + 4z
- Milk : Water = 2 : 3
Therefore, the ratio of
We are given three vessels of 20 litres capacity each filled with a mixture of milk and water in different ratios. We need to find the ratio of milk and water in the final mixture when all the three vessels are emptied into a fourth vessel.
Given:
- Three vessels of 20 litres capacity filled with mixtures of milk and water in the ratios of 2:3, 3:4, and 4:5 respectively.
To find:
- The ratio of milk and water in the final mixture when all the three vessels are emptied into a fourth vessel.
Solution:
Let us assume that the amount of milk and water in each vessel is proportional to the given ratios. Therefore, we can write:
- First vessel: Milk = 2x litres and Water = 3x litres
- Second vessel: Milk = 3y litres and Water = 4y litres
- Third vessel: Milk = 4z litres and Water = 5z litres
Now, when all the three vessels are emptied into a fourth vessel, the total amount of milk and water in the fourth vessel will be:
- Milk = 2x + 3y + 4z litres
- Water = 3x + 4y + 5z litres
We know that the total capacity of the fourth vessel is 60 litres (20 litres x 3 vessels). Therefore, we can write:
- Milk + Water = 60
- 2x + 3y + 4z + 3x + 4y + 5z = 60
- 5x + 7y + 9z = 60
Now, we need to find the ratio of milk and water in the final mixture. Therefore, we can write:
- Milk : Water = (2x + 3y + 4z) : (3x + 4y + 5z)
- Milk : Water = (2x + 3y + 4z) / (3x + 4y + 5z) : 1
Substituting the value of (5x + 7y + 9z) = 60, we get:
- Milk : Water = (2x + 3y + 4z) / (3x + 4y + 5z) : 1
- Milk : Water = (2x + 3y + 4z) / (5x + 7y + 9z - 2x - 3y - 4z) : 1
- Milk : Water = (2x + 3y + 4z) / (3x + 4y + 5z) : (5x + 7y + 9z - 2x - 3y - 4z) / (3x + 4y + 5z)
- Milk : Water = (2x + 3y + 4z) / (3x + 4y + 5z) : (3x + 3y + 4z) / (3x + 4y + 5z)
- Milk : Water = 2x + 3y + 4z : 3x + 3y + 4z
- Milk : Water = 2 : 3
Therefore, the ratio of
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