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A can contains milk and water in the ratio 3:1. A part of this mixture is replaced with milk, and now the new ratio of milk to water is 15:4.What proportion of original mixture had been replaced by milk?
- a)9/19
- b)8/19
- c)6/17
- d)3/19
- e)4/19
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A can contains milk and water in the ratio 3:1. A part of this mixture...
D) 3/19
Explanation: Let total original quantity = x litres, Let y litres replaced.
After y litres of mixture drawn out, Milk = [3/(3+1)] * x – [3/(3+1)] * y Water = [1/(3+1)] * x – [1/(3+1)] * y Now y litres of milk poured in can. Milk becomes (3/4)*x – (3/4)*y +y = (3/4)*x + (1/4)*y Now [(3/4)*x +(1/4)*y] / [(1/4)*x – (1/4)*y] = 15/4 Solve, y = (3/19)* x So 3/19 of original mixture removed.
Explanation: Let total original quantity = x litres, Let y litres replaced.
After y litres of mixture drawn out, Milk = [3/(3+1)] * x – [3/(3+1)] * y Water = [1/(3+1)] * x – [1/(3+1)] * y Now y litres of milk poured in can. Milk becomes (3/4)*x – (3/4)*y +y = (3/4)*x + (1/4)*y Now [(3/4)*x +(1/4)*y] / [(1/4)*x – (1/4)*y] = 15/4 Solve, y = (3/19)* x So 3/19 of original mixture removed.
Most Upvoted Answer
A can contains milk and water in the ratio 3:1. A part of this mixture...
D) 3/19
Explanation: Let total original quantity = x litres, Let y litres replaced.
After y litres of mixture drawn out, Milk = [3/(3+1)] * x – [3/(3+1)] * y Water = [1/(3+1)] * x – [1/(3+1)] * y Now y litres of milk poured in can. Milk becomes (3/4)*x – (3/4)*y +y = (3/4)*x + (1/4)*y Now [(3/4)*x +(1/4)*y] / [(1/4)*x – (1/4)*y] = 15/4 Solve, y = (3/19)* x So 3/19 of original mixture removed.
Explanation: Let total original quantity = x litres, Let y litres replaced.
After y litres of mixture drawn out, Milk = [3/(3+1)] * x – [3/(3+1)] * y Water = [1/(3+1)] * x – [1/(3+1)] * y Now y litres of milk poured in can. Milk becomes (3/4)*x – (3/4)*y +y = (3/4)*x + (1/4)*y Now [(3/4)*x +(1/4)*y] / [(1/4)*x – (1/4)*y] = 15/4 Solve, y = (3/19)* x So 3/19 of original mixture removed.
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Community Answer
A can contains milk and water in the ratio 3:1. A part of this mixture...
Given:
- The original ratio of milk to water in the can is 3:1.
- A part of this mixture is replaced with milk.
- The new ratio of milk to water after the replacement is 15:4.
To find:
- The proportion of the original mixture that had been replaced by milk.
Assumption:
Let's assume that the original quantity of the mixture is 4 units (since the ratio is given as 3:1).
Step 1: Calculate the original quantity of milk and water
- The original ratio of milk to water is 3:1, so the original quantity of milk is (3/4) * 4 = 3 units.
- The original quantity of water is (1/4) * 4 = 1 unit.
Step 2: Calculate the new quantity of milk and water
- After the replacement, the new ratio of milk to water is 15:4.
- Let's assume that x units of the original mixture are replaced by milk.
- So, the new quantity of milk is 3 + x units and the new quantity of water is 1 unit.
Step 3: Set up the equation
- According to the given information, the new ratio of milk to water is 15:4.
- This can be represented as (3 + x)/1 = 15/4.
- Cross-multiplying, we get 4(3 + x) = 15 * 1.
- Simplifying, we get 12 + 4x = 15.
- Solving for x, we get x = 3/4.
Step 4: Calculate the proportion of the original mixture replaced
- We assumed that the original quantity of the mixture is 4 units.
- The quantity replaced is x = 3/4 units.
- The proportion of the original mixture replaced is (3/4) / 4 = 3/16.
- Simplifying, we get 3/16 = 3/4 * 1/4 = 3/16.
Therefore, the proportion of the original mixture that had been replaced by milk is 3/16, which is equivalent to 3/19 (after simplifying). Hence, the correct answer is option (D) 3/19.
- The original ratio of milk to water in the can is 3:1.
- A part of this mixture is replaced with milk.
- The new ratio of milk to water after the replacement is 15:4.
To find:
- The proportion of the original mixture that had been replaced by milk.
Assumption:
Let's assume that the original quantity of the mixture is 4 units (since the ratio is given as 3:1).
Step 1: Calculate the original quantity of milk and water
- The original ratio of milk to water is 3:1, so the original quantity of milk is (3/4) * 4 = 3 units.
- The original quantity of water is (1/4) * 4 = 1 unit.
Step 2: Calculate the new quantity of milk and water
- After the replacement, the new ratio of milk to water is 15:4.
- Let's assume that x units of the original mixture are replaced by milk.
- So, the new quantity of milk is 3 + x units and the new quantity of water is 1 unit.
Step 3: Set up the equation
- According to the given information, the new ratio of milk to water is 15:4.
- This can be represented as (3 + x)/1 = 15/4.
- Cross-multiplying, we get 4(3 + x) = 15 * 1.
- Simplifying, we get 12 + 4x = 15.
- Solving for x, we get x = 3/4.
Step 4: Calculate the proportion of the original mixture replaced
- We assumed that the original quantity of the mixture is 4 units.
- The quantity replaced is x = 3/4 units.
- The proportion of the original mixture replaced is (3/4) / 4 = 3/16.
- Simplifying, we get 3/16 = 3/4 * 1/4 = 3/16.
Therefore, the proportion of the original mixture that had been replaced by milk is 3/16, which is equivalent to 3/19 (after simplifying). Hence, the correct answer is option (D) 3/19.
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