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When one litre of water is added to a mixture of milk and water, the new mixture contains 25% of milk. When one litre of milk is added to the new mixture, then the resulting mixture contains 40% milk. What is the percentage of milk in the original mixture?
- a)100/6 %
- b)50/6 %
- c)100/3 %
- d)50/3 %
- e)None of the Above
Correct answer is option 'C'. Can you explain this answer?
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When one litre of water is added to a mixture of milk and water, the n...
Answer – C. 100/3 % Explanation : Original Mixture = x L In (x + 1) Mixture, quantity of milk = (x + 1)* (25/100) = (x + 1)/4 one litre of milk is added to the new mixture [((x + 1)/4 )+ 1 ]/ x + 2 = 40% x = 3 ; quantity of milk = (3 + 1)/4 = 1L percentage of milk in the original mixture = 1/3 * 100 = 100/3 %
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When one litre of water is added to a mixture of milk and water, the n...
Problem: When one litre of water is added to a mixture of milk and water, the new mixture contains 25% of milk. When one litre of milk is added to the new mixture, then the resulting mixture contains 40% milk. What is the percentage of milk in the original mixture?
Solution:
Let us assume that the amount of milk in the original mixture is x litres, and the amount of water is y litres.
Step 1: First, we need to find out the milk and water content in the new mixture after adding one litre of water.
- After adding one litre of water to the original mixture, the total volume becomes (x+y+1) litres.
- As per the given condition, the new mixture contains 25% milk. Therefore, the amount of milk in the new mixture is 25% of (x+y+1) litres, which is 0.25(x+y+1) litres.
- The remaining part of the new mixture is water. Therefore, the amount of water in the new mixture is (x+y+1) - 0.25(x+y+1) = 0.75(x+y+1) litres.
Step 2: Next, we need to find out the milk and water content in the final mixture after adding one litre of milk to the new mixture.
- After adding one litre of milk to the new mixture, the total volume becomes (x+y+2) litres.
- As per the given condition, the final mixture contains 40% milk. Therefore, the amount of milk in the final mixture is 40% of (x+y+2) litres, which is 0.4(x+y+2) litres.
- The remaining part of the final mixture is water. Therefore, the amount of water in the final mixture is (x+y+2) - 0.4(x+y+2) = 0.6(x+y+2) litres.
Step 3: Now, we can form two equations based on the above calculations and solve them to find the values of x and y.
Equation 1: 0.25(x+y+1) + y = (x+y+1) [Equation based on the first condition]
Simplifying the above equation, we get:
x = 3y + 1
Equation 2: 0.4(x+y+2) = x + y + 2 [Equation based on the second condition]
Substituting the value of x from equation 1 in equation 2, we get:
y = 3
Therefore, the amount of milk in the original mixture is x = 3y + 1 = 10 litres.
The total volume of the original mixture is x + y = 13 litres.
Hence, the percentage of milk in the original mixture is (10/13) x 100 = 76.92%, which is approximately equal to 100/3%.
Answer: Option (c) 100/3%.
Solution:
Let us assume that the amount of milk in the original mixture is x litres, and the amount of water is y litres.
Step 1: First, we need to find out the milk and water content in the new mixture after adding one litre of water.
- After adding one litre of water to the original mixture, the total volume becomes (x+y+1) litres.
- As per the given condition, the new mixture contains 25% milk. Therefore, the amount of milk in the new mixture is 25% of (x+y+1) litres, which is 0.25(x+y+1) litres.
- The remaining part of the new mixture is water. Therefore, the amount of water in the new mixture is (x+y+1) - 0.25(x+y+1) = 0.75(x+y+1) litres.
Step 2: Next, we need to find out the milk and water content in the final mixture after adding one litre of milk to the new mixture.
- After adding one litre of milk to the new mixture, the total volume becomes (x+y+2) litres.
- As per the given condition, the final mixture contains 40% milk. Therefore, the amount of milk in the final mixture is 40% of (x+y+2) litres, which is 0.4(x+y+2) litres.
- The remaining part of the final mixture is water. Therefore, the amount of water in the final mixture is (x+y+2) - 0.4(x+y+2) = 0.6(x+y+2) litres.
Step 3: Now, we can form two equations based on the above calculations and solve them to find the values of x and y.
Equation 1: 0.25(x+y+1) + y = (x+y+1) [Equation based on the first condition]
Simplifying the above equation, we get:
x = 3y + 1
Equation 2: 0.4(x+y+2) = x + y + 2 [Equation based on the second condition]
Substituting the value of x from equation 1 in equation 2, we get:
y = 3
Therefore, the amount of milk in the original mixture is x = 3y + 1 = 10 litres.
The total volume of the original mixture is x + y = 13 litres.
Hence, the percentage of milk in the original mixture is (10/13) x 100 = 76.92%, which is approximately equal to 100/3%.
Answer: Option (c) 100/3%.
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