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M litres of milk solution contains 80% milk. Instead of adding certain amount of water to change the 80% milk solution to 60% milk solution, same amount of milk is added by mistake. To the resulting solution W litres of water is added and the initial objective of 60% milk solution is attained. What is the ratio of M and W.
- a)8:5
- b)9:5
- c)2:1
- d)11:5
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
M litres of milk solution contains 80% milk. Instead of adding certai...
To solve this problem, let's break it down step by step:
Step 1: Initial Solution
We are given that the initial solution contains M litres of milk solution with 80% milk. This means that 80% of M litres is milk, and the remaining 20% is water.
Step 2: Adding Milk by Mistake
Instead of adding water to change the 80% milk solution to a 60% milk solution, the same amount of milk is added by mistake. This means that the amount of milk in the solution remains the same, but the total volume of the solution increases.
Step 3: Adding Water
To attain the objective of a 60% milk solution, we need to add water to the resulting solution. Let's assume that the amount of water added is W litres.
Step 4: Final Solution
After adding water, the total volume of the solution becomes M + W litres. Since the objective is to have a 60% milk solution, we know that 60% of the final volume should be milk, and the remaining 40% should be water.
Step 5: Calculating the Ratio
To find the ratio of M and W, we need to equate the amount of milk in the initial solution and the final solution.
In the initial solution, 80% of M litres is milk, so the amount of milk is 0.8M litres.
In the final solution, 60% of the total volume (M + W) is milk, so the amount of milk is 0.6(M + W) litres.
Since the amount of milk remains the same in both the initial and final solutions, we can equate the two expressions:
0.8M = 0.6(M + W)
Simplifying the equation:
0.8M = 0.6M + 0.6W
0.2M = 0.6W
M = 3W
Therefore, the ratio of M to W is 3:1, which can be simplified to 9:3 or 9:5. Hence, the correct answer is option B) 9:5.
Step 1: Initial Solution
We are given that the initial solution contains M litres of milk solution with 80% milk. This means that 80% of M litres is milk, and the remaining 20% is water.
Step 2: Adding Milk by Mistake
Instead of adding water to change the 80% milk solution to a 60% milk solution, the same amount of milk is added by mistake. This means that the amount of milk in the solution remains the same, but the total volume of the solution increases.
Step 3: Adding Water
To attain the objective of a 60% milk solution, we need to add water to the resulting solution. Let's assume that the amount of water added is W litres.
Step 4: Final Solution
After adding water, the total volume of the solution becomes M + W litres. Since the objective is to have a 60% milk solution, we know that 60% of the final volume should be milk, and the remaining 40% should be water.
Step 5: Calculating the Ratio
To find the ratio of M and W, we need to equate the amount of milk in the initial solution and the final solution.
In the initial solution, 80% of M litres is milk, so the amount of milk is 0.8M litres.
In the final solution, 60% of the total volume (M + W) is milk, so the amount of milk is 0.6(M + W) litres.
Since the amount of milk remains the same in both the initial and final solutions, we can equate the two expressions:
0.8M = 0.6(M + W)
Simplifying the equation:
0.8M = 0.6M + 0.6W
0.2M = 0.6W
M = 3W
Therefore, the ratio of M to W is 3:1, which can be simplified to 9:3 or 9:5. Hence, the correct answer is option B) 9:5.
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Community Answer
M litres of milk solution contains 80% milk. Instead of adding certai...
The milk solution contains 20% water.
To make 80% milk solution to 60% milk solution, one needs to add(40 - 20):(100 - 40) i.e. 1/3M water.
However by mistake 1/3M milk is added which will result in 0.8M + 1/3M i.e. 3.4M/3
Litres of milk with a total volume of the solution = M + 1/3M i.e. 4M/3.
Now W Litres of water is added to make the concentration of milk to 60%.
So, 3.4M/3 = 0.6*(4M/3 + W) = 2.4M/3 + 0.6W
So, M/3 = 0.6W
So M/W = 1.8 = 9:5
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M litres of milk solution contains 80% milk. Instead of adding certain amount of water to change the 80% milk solution to 60% milk solution, same amount of milk is added by mistake. To the resulting solution W litres of water is added and the initial objective of 60% milk solution is attained. What is the ratio of M and W.a)8:5b)9:5c)2:1d)11:5Correct answer is option 'B'. Can you explain this answer?
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M litres of milk solution contains 80% milk. Instead of adding certain amount of water to change the 80% milk solution to 60% milk solution, same amount of milk is added by mistake. To the resulting solution W litres of water is added and the initial objective of 60% milk solution is attained. What is the ratio of M and W.a)8:5b)9:5c)2:1d)11:5Correct answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about M litres of milk solution contains 80% milk. Instead of adding certain amount of water to change the 80% milk solution to 60% milk solution, same amount of milk is added by mistake. To the resulting solution W litres of water is added and the initial objective of 60% milk solution is attained. What is the ratio of M and W.a)8:5b)9:5c)2:1d)11:5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for M litres of milk solution contains 80% milk. Instead of adding certain amount of water to change the 80% milk solution to 60% milk solution, same amount of milk is added by mistake. To the resulting solution W litres of water is added and the initial objective of 60% milk solution is attained. What is the ratio of M and W.a)8:5b)9:5c)2:1d)11:5Correct answer is option 'B'. Can you explain this answer?.
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