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A sample of x litre is replaced from a container containing milk and water in the ratio 2:3 by pure milk. If the container hold 30 litres of the mixture, and after the operation proportion of milk and water is same. Find the value of X?
- a)4
- b)5
- c)6
- d)7
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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A sample of x litre is replaced from a container containing milk and w...
Answer – b) 5 Explanation : milk = 30*2/5 = 12 and water = 30*3/5 = 18 milk = 12 – x*2/5 + x and water = 18 – x*3/5 equate both equation and we get x = 5
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A sample of x litre is replaced from a container containing milk and w...
Question:
Find the value of X if a sample of x litre is replaced from a container containing milk and water in the ratio 2:3 by pure milk. If the container hold 30 litres of the mixture, and after the operation proportion of milk and water is same.
Solution:
Let us assume that the container initially contains 2x litres of milk and 3x litres of water. Therefore, the total quantity of the mixture is 2x+3x = 5x litres.
Now, x litres of the mixture is replaced with pure milk. Therefore, the quantity of milk in the container becomes 2x-x = x litres and the quantity of water remains 3x litres.
After the replacement, the container holds 30 litres of the mixture. Therefore, we have:
x+3x = 30
4x = 30
x = 7.5
Therefore, initially, the container contained 2x = 15 litres of milk and 3x = 22.5 litres of water.
After x litres of the mixture is replaced with pure milk, the container contains x = 7.5 litres of milk and 22.5 litres of water.
Now, the proportion of milk and water in the container is:
Milk: (7.5/30) = 1/4
Water: (22.5/30) = 3/4
The proportion of milk and water is the same before and after the replacement. Hence, the correct answer is option B) 5.
Find the value of X if a sample of x litre is replaced from a container containing milk and water in the ratio 2:3 by pure milk. If the container hold 30 litres of the mixture, and after the operation proportion of milk and water is same.
Solution:
Let us assume that the container initially contains 2x litres of milk and 3x litres of water. Therefore, the total quantity of the mixture is 2x+3x = 5x litres.
Now, x litres of the mixture is replaced with pure milk. Therefore, the quantity of milk in the container becomes 2x-x = x litres and the quantity of water remains 3x litres.
After the replacement, the container holds 30 litres of the mixture. Therefore, we have:
x+3x = 30
4x = 30
x = 7.5
Therefore, initially, the container contained 2x = 15 litres of milk and 3x = 22.5 litres of water.
After x litres of the mixture is replaced with pure milk, the container contains x = 7.5 litres of milk and 22.5 litres of water.
Now, the proportion of milk and water in the container is:
Milk: (7.5/30) = 1/4
Water: (22.5/30) = 3/4
The proportion of milk and water is the same before and after the replacement. Hence, the correct answer is option B) 5.
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