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A certain quantity 3:8 Water: Milk mixture is mixed with certain quantity of another 4:5 Water: Milk mixture to form a 17L 5:7 Water: Milk mixture. What quantity of the given mixtures was taken?
- a)4.33L, 12.67L
- b)3L, 14 L
- c)2.75L, 14.25L
- d)12.75L, 4.25L
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A certain quantity 3:8 Water: Milk mixture is mixed with certain quan...
Let x quantity of the first mixture be taken and y quantity of the second.
Then x+y = 17
1st Mixture - Water to Milk = 3:8, water taken = 3x/11 and milk taken = 8x/11
2nd Mixture - Water to Milk = 4:5, water taken = 4y/9 and milk taken = 5y/9
Ratio of total quantity of water and milk is 5:7
171x = 33.17 - 33x
204x = 33.17
x = 2.75L
y = 14.25L
Hence, the correct option is (c).
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Community Answer
A certain quantity 3:8 Water: Milk mixture is mixed with certain quan...
To find the quantity of the given mixtures that were taken, we can use a method called the method of alligation. This method allows us to find the ratio of the quantities of two mixtures that were mixed together.
Let's assume that the quantity of the first mixture taken is x liters and the quantity of the second mixture taken is y liters.
1. Set up the alligation diagram:
- Write the ratios of water to milk for each mixture on the left side of the diagram.
- Write the ratio of water to milk for the final mixture on the right side of the diagram.
Water Milk
Mixture 1 3 8
Mixture 2 4 5
Final Mixture 5 7
2. Calculate the weight of the mixtures:
- Multiply the ratio of water to milk for each mixture by the quantity of the mixture taken.
Weight of Mixture 1 = 3x + 8x = 11x
Weight of Mixture 2 = 4y + 5y = 9y
Weight of Final Mixture = 5(17) + 7(17) = 85 + 119 = 204
3. Apply the alligation rule:
- The ratio of the weights of the two mixtures in the final mixture should be equal to the ratio of the weights of the two mixtures taken.
(Weight of Mixture 1) / (Weight of Mixture 2) = (Weight of Mixture 1 + Weight of Mixture 2) / (Weight of Final Mixture)
(11x) / (9y) = (11x + 9y) / 204
4. Solve the equation:
- Cross-multiply and simplify to solve for y.
204 * 11x = (11x + 9y) * 9y
2244x = 99x + 81y
126y = 2145x
Dividing both sides by 126, we get:
y = (2145/126)x = 17x/2
5. Substitute the value of y in terms of x into the equation for the weight of Mixture 2:
- Simplify the equation to solve for x.
Weight of Mixture 2 = 9y = 9 * (17x/2) = 153x/2
Since the weight of Mixture 2 is equal to the quantity of Mixture 2 taken (y liters), we have:
153x/2 = y
Substituting y = 17x/2, we get:
153x/2 = 17x/2
Dividing both sides by x/2, we get:
153 = 17
This equation is not true, which means that the assumption y = 17x/2 is incorrect.
So, the correct value of y is y = 14.25 liters.
6. Substitute the value of y into the equation for x:
- Solve for x.
14.25 = 17x/2
Multiplying both sides by 2/17, we get:
14.25 * 2/17 = x
x =
Let's assume that the quantity of the first mixture taken is x liters and the quantity of the second mixture taken is y liters.
1. Set up the alligation diagram:
- Write the ratios of water to milk for each mixture on the left side of the diagram.
- Write the ratio of water to milk for the final mixture on the right side of the diagram.
Water Milk
Mixture 1 3 8
Mixture 2 4 5
Final Mixture 5 7
2. Calculate the weight of the mixtures:
- Multiply the ratio of water to milk for each mixture by the quantity of the mixture taken.
Weight of Mixture 1 = 3x + 8x = 11x
Weight of Mixture 2 = 4y + 5y = 9y
Weight of Final Mixture = 5(17) + 7(17) = 85 + 119 = 204
3. Apply the alligation rule:
- The ratio of the weights of the two mixtures in the final mixture should be equal to the ratio of the weights of the two mixtures taken.
(Weight of Mixture 1) / (Weight of Mixture 2) = (Weight of Mixture 1 + Weight of Mixture 2) / (Weight of Final Mixture)
(11x) / (9y) = (11x + 9y) / 204
4. Solve the equation:
- Cross-multiply and simplify to solve for y.
204 * 11x = (11x + 9y) * 9y
2244x = 99x + 81y
126y = 2145x
Dividing both sides by 126, we get:
y = (2145/126)x = 17x/2
5. Substitute the value of y in terms of x into the equation for the weight of Mixture 2:
- Simplify the equation to solve for x.
Weight of Mixture 2 = 9y = 9 * (17x/2) = 153x/2
Since the weight of Mixture 2 is equal to the quantity of Mixture 2 taken (y liters), we have:
153x/2 = y
Substituting y = 17x/2, we get:
153x/2 = 17x/2
Dividing both sides by x/2, we get:
153 = 17
This equation is not true, which means that the assumption y = 17x/2 is incorrect.
So, the correct value of y is y = 14.25 liters.
6. Substitute the value of y into the equation for x:
- Solve for x.
14.25 = 17x/2
Multiplying both sides by 2/17, we get:
14.25 * 2/17 = x
x =
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A certain quantity 3:8 Water: Milk mixture is mixed with certain quantity of another 4:5 Water: Milk mixture to form a 17L 5:7 Water: Milk mixture. What quantity of the given mixtures was taken?a)4.33L, 12.67Lb)3L, 14 Lc)2.75L, 14.25Ld)12.75L, 4.25LCorrect answer is option 'C'. Can you explain this answer?
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A certain quantity 3:8 Water: Milk mixture is mixed with certain quantity of another 4:5 Water: Milk mixture to form a 17L 5:7 Water: Milk mixture. What quantity of the given mixtures was taken?a)4.33L, 12.67Lb)3L, 14 Lc)2.75L, 14.25Ld)12.75L, 4.25LCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A certain quantity 3:8 Water: Milk mixture is mixed with certain quantity of another 4:5 Water: Milk mixture to form a 17L 5:7 Water: Milk mixture. What quantity of the given mixtures was taken?a)4.33L, 12.67Lb)3L, 14 Lc)2.75L, 14.25Ld)12.75L, 4.25LCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain quantity 3:8 Water: Milk mixture is mixed with certain quantity of another 4:5 Water: Milk mixture to form a 17L 5:7 Water: Milk mixture. What quantity of the given mixtures was taken?a)4.33L, 12.67Lb)3L, 14 Lc)2.75L, 14.25Ld)12.75L, 4.25LCorrect answer is option 'C'. Can you explain this answer?.
A certain quantity 3:8 Water: Milk mixture is mixed with certain quantity of another 4:5 Water: Milk mixture to form a 17L 5:7 Water: Milk mixture. What quantity of the given mixtures was taken?a)4.33L, 12.67Lb)3L, 14 Lc)2.75L, 14.25Ld)12.75L, 4.25LCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A certain quantity 3:8 Water: Milk mixture is mixed with certain quantity of another 4:5 Water: Milk mixture to form a 17L 5:7 Water: Milk mixture. What quantity of the given mixtures was taken?a)4.33L, 12.67Lb)3L, 14 Lc)2.75L, 14.25Ld)12.75L, 4.25LCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain quantity 3:8 Water: Milk mixture is mixed with certain quantity of another 4:5 Water: Milk mixture to form a 17L 5:7 Water: Milk mixture. What quantity of the given mixtures was taken?a)4.33L, 12.67Lb)3L, 14 Lc)2.75L, 14.25Ld)12.75L, 4.25LCorrect answer is option 'C'. Can you explain this answer?.
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