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Two equal glasses filled with mixtures of milk and water in the proportions of 2 : 1 and 1 : 1 respectively were emptied into third glass. What is the proportion of milk and water in the third glass?
- a)5 : 7
- b)7 : 5
- c)7 : 6
- d)6 : 7
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two equal glasses filled with mixtures of milk and water in the propor...
⇒ Let the quantity of milk and water in 1st and 2nd vessel be 2x, x and x, x respectively.
⇒ Milk in the first mixture = 2x/(2x + x) = 2/3
⇒ Water in the first mixture = x/(2x + x) = 1/3
⇒ Milk in the Second mixture = x/(x + x) = 1/2
⇒ Water in the second mixture = x/(x + x) = 1/2
⇒ Ratio of Milk and water in new mixture = (2/3 + 1/2)/(1/3 + 1/2)
⇒ Ratio of Milk and water in new mixture = {(2 × 2 + 1 × 3)/6}/{(2 × 1 + 3 × 1)/6}
⇒ Ratio of Milk and water in new mixture = (7)/(5)
∴ Ratio of Milk and water in new mixture = 7 : 5
Most Upvoted Answer
Two equal glasses filled with mixtures of milk and water in the propor...
Proportion of milk and water in the third glass:
Let's assume that each glass contains 3 units of the mixture (since the proportions are given as 2:1 and 1:1).
So, the first glass contains 2 units of milk and 1 unit of water, and the second glass contains 1 unit of milk and 1 unit of water.
When both glasses are emptied into the third glass, the total volume of the mixture in the third glass will be 6 units (3 units from each glass).
To find the proportion of milk and water in the third glass, we need to determine the total amount of milk and water present in the mixture.
- Total milk: In the first glass, there are 2 units of milk, and in the second glass, there is 1 unit of milk. So, the total milk in the third glass is 2 + 1 = 3 units.
- Total water: In the first glass, there is 1 unit of water, and in the second glass, there is 1 unit of water. So, the total water in the third glass is 1 + 1 = 2 units.
Therefore, the proportion of milk and water in the third glass is 3:2.
Now, we can simplify this ratio by dividing both the numerator and denominator by the highest common factor, which is 1.
Dividing 3 and 2 by 1, we get the simplified ratio as 3/1 : 2/1.
Simplifying further, we get 3 : 2.
Hence, the proportion of milk and water in the third glass is 3 : 2, which can be written as 7 : 5.
Therefore, the correct answer is option B) 7 : 5.
Let's assume that each glass contains 3 units of the mixture (since the proportions are given as 2:1 and 1:1).
So, the first glass contains 2 units of milk and 1 unit of water, and the second glass contains 1 unit of milk and 1 unit of water.
When both glasses are emptied into the third glass, the total volume of the mixture in the third glass will be 6 units (3 units from each glass).
To find the proportion of milk and water in the third glass, we need to determine the total amount of milk and water present in the mixture.
- Total milk: In the first glass, there are 2 units of milk, and in the second glass, there is 1 unit of milk. So, the total milk in the third glass is 2 + 1 = 3 units.
- Total water: In the first glass, there is 1 unit of water, and in the second glass, there is 1 unit of water. So, the total water in the third glass is 1 + 1 = 2 units.
Therefore, the proportion of milk and water in the third glass is 3:2.
Now, we can simplify this ratio by dividing both the numerator and denominator by the highest common factor, which is 1.
Dividing 3 and 2 by 1, we get the simplified ratio as 3/1 : 2/1.
Simplifying further, we get 3 : 2.
Hence, the proportion of milk and water in the third glass is 3 : 2, which can be written as 7 : 5.
Therefore, the correct answer is option B) 7 : 5.
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Two equal glasses filled with mixtures of milk and water in the proportions of 2 : 1 and 1 : 1 respectively were emptied into third glass. What is the proportion of milk and water in the third glass?a)5 : 7b)7 : 5c)7 : 6d)6 : 7Correct answer is option 'B'. Can you explain this answer?
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