CAT Exam > CAT Questions > If a mixture of milk and water contains milk ...
Start Learning for Free
If a mixture of milk and water contains milk and water in the ratio 7:2, as mixture contains milk and water in the ratio 5:3, in what ratio should the two mixtures be mixed so that the ratio of water & milk becomes 3:7?
Most Upvoted Answer
If a mixture of milk and water contains milk and water in the ratio 7:...
Let's assume that we have x units of the first mixture and y units of the second mixture.
According to the problem, the first mixture has milk and water in the ratio 7:2. This means that out of every 9 units of the mixture, 7 units are milk and 2 units are water. Therefore, the amount of milk in x units of the first mixture is (7/9)x and the amount of water is (2/9)x.
Similarly, the second mixture has milk and water in the ratio 5:3. This means that out of every 8 units of the mixture, 5 units are milk and 3 units are water. Therefore, the amount of milk in y units of the second mixture is (5/8)y and the amount of water is (3/8)y.
When these two mixtures are combined, the total amount of milk is (7/9)x + (5/8)y and the total amount of water is (2/9)x + (3/8)y.
We want to find the ratio of water to milk in the final mixture. This is given by:
(2/9)x + (3/8)y : (7/9)x + (5/8)y
To simplify this expression, we can cross-multiply:
(2/9)x + (3/8)y = k(7/9)x + k(5/8)y
where k is the ratio in which the two mixtures are mixed.
Simplifying this equation, we get:
(2/9)x - k(7/9)x = k(5/8)y - (3/8)y
(2-7k)/9 x = (5k-3)/8 y
We can now solve for k:
k = [(5/8)y - (3/8)y]/[(2/9)x - (7/9)x]
k = (2/9)y / (-5/9)x
k = -2/5
Therefore, the two mixtures should be mixed in the ratio 2:3 (or 2 parts of the first mixture to 3 parts of the second mixture) so that the ratio of water to milk in the final mixture is 3:7.
According to the problem, the first mixture has milk and water in the ratio 7:2. This means that out of every 9 units of the mixture, 7 units are milk and 2 units are water. Therefore, the amount of milk in x units of the first mixture is (7/9)x and the amount of water is (2/9)x.
Similarly, the second mixture has milk and water in the ratio 5:3. This means that out of every 8 units of the mixture, 5 units are milk and 3 units are water. Therefore, the amount of milk in y units of the second mixture is (5/8)y and the amount of water is (3/8)y.
When these two mixtures are combined, the total amount of milk is (7/9)x + (5/8)y and the total amount of water is (2/9)x + (3/8)y.
We want to find the ratio of water to milk in the final mixture. This is given by:
(2/9)x + (3/8)y : (7/9)x + (5/8)y
To simplify this expression, we can cross-multiply:
(2/9)x + (3/8)y = k(7/9)x + k(5/8)y
where k is the ratio in which the two mixtures are mixed.
Simplifying this equation, we get:
(2/9)x - k(7/9)x = k(5/8)y - (3/8)y
(2-7k)/9 x = (5k-3)/8 y
We can now solve for k:
k = [(5/8)y - (3/8)y]/[(2/9)x - (7/9)x]
k = (2/9)y / (-5/9)x
k = -2/5
Therefore, the two mixtures should be mixed in the ratio 2:3 (or 2 parts of the first mixture to 3 parts of the second mixture) so that the ratio of water to milk in the final mixture is 3:7.
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
If a mixture of milk and water contains milk and water in the ratio 7:2, as mixture contains milk and water in the ratio 5:3, in what ratio should the two mixtures be mixed so that the ratio of water & milk becomes 3:7?
Question Description
If a mixture of milk and water contains milk and water in the ratio 7:2, as mixture contains milk and water in the ratio 5:3, in what ratio should the two mixtures be mixed so that the ratio of water & milk becomes 3:7? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If a mixture of milk and water contains milk and water in the ratio 7:2, as mixture contains milk and water in the ratio 5:3, in what ratio should the two mixtures be mixed so that the ratio of water & milk becomes 3:7? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a mixture of milk and water contains milk and water in the ratio 7:2, as mixture contains milk and water in the ratio 5:3, in what ratio should the two mixtures be mixed so that the ratio of water & milk becomes 3:7?.
If a mixture of milk and water contains milk and water in the ratio 7:2, as mixture contains milk and water in the ratio 5:3, in what ratio should the two mixtures be mixed so that the ratio of water & milk becomes 3:7? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If a mixture of milk and water contains milk and water in the ratio 7:2, as mixture contains milk and water in the ratio 5:3, in what ratio should the two mixtures be mixed so that the ratio of water & milk becomes 3:7? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a mixture of milk and water contains milk and water in the ratio 7:2, as mixture contains milk and water in the ratio 5:3, in what ratio should the two mixtures be mixed so that the ratio of water & milk becomes 3:7?.
Solutions for If a mixture of milk and water contains milk and water in the ratio 7:2, as mixture contains milk and water in the ratio 5:3, in what ratio should the two mixtures be mixed so that the ratio of water & milk becomes 3:7? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of If a mixture of milk and water contains milk and water in the ratio 7:2, as mixture contains milk and water in the ratio 5:3, in what ratio should the two mixtures be mixed so that the ratio of water & milk becomes 3:7? defined & explained in the simplest way possible. Besides giving the explanation of
If a mixture of milk and water contains milk and water in the ratio 7:2, as mixture contains milk and water in the ratio 5:3, in what ratio should the two mixtures be mixed so that the ratio of water & milk becomes 3:7?, a detailed solution for If a mixture of milk and water contains milk and water in the ratio 7:2, as mixture contains milk and water in the ratio 5:3, in what ratio should the two mixtures be mixed so that the ratio of water & milk becomes 3:7? has been provided alongside types of If a mixture of milk and water contains milk and water in the ratio 7:2, as mixture contains milk and water in the ratio 5:3, in what ratio should the two mixtures be mixed so that the ratio of water & milk becomes 3:7? theory, EduRev gives you an
ample number of questions to practice If a mixture of milk and water contains milk and water in the ratio 7:2, as mixture contains milk and water in the ratio 5:3, in what ratio should the two mixtures be mixed so that the ratio of water & milk becomes 3:7? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup