CAT Exam  >  CAT Questions  >  Two vessels contain mixtures of milk and wate... Start Learning for Free
Two vessels contain mixtures of milk and water in ratios 8 : 1 and 1 : 5, respectively. The contents of both of these are mixed in a specific ratio into a third vessel. How much mixture should be drawn from the second vessel to fill the third vessel (capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?
  • a)
    12 gallons
  • b)
    14 gallons
  • c)
    10 gallons
  • d)
    13 gallons
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Two vessels contain mixtures of milk and water in ratios 8 : 1 and 1 :...
Let x litres of the first mixture be mixed with y litres of the second mixture.
Milk Water
Since the third vessel contains half milk and half water;
16x + 3y = 2x + 15y
14x = 12y
x/y = 12/14 = 6/7
Hence, y = 7 /(7+ 6) of 26 gallons = 7/13 x 26 = 14 gallons
Free Test
Community Answer
Two vessels contain mixtures of milk and water in ratios 8 : 1 and 1 :...
Given:
- Ratio of milk to water in the first vessel = 8 : 1
- Ratio of milk to water in the second vessel = 1 : 5
- Capacity of the third vessel = 26 gallons
- The resulting mixture in the third vessel should be half milk and half water

To find:
- How much mixture should be drawn from the second vessel to fill the third vessel completely?

Solution:
Let's assume that x gallons of mixture is drawn from the second vessel to fill the third vessel.

Calculating the ratio of milk to water in the third vessel:
- The first vessel contains a mixture in the ratio of 8 : 1, which means it contains 8/9 milk and 1/9 water.
- The second vessel contains a mixture in the ratio of 1 : 5, which means it contains 1/6 milk and 5/6 water.
- When x gallons of mixture is drawn from the second vessel, it will contain (1/6)x gallons of milk and (5/6)x gallons of water.

The total milk and water in the third vessel can be calculated as follows:

- Milk in the first vessel = (8/9) * 26 gallons
- Milk in the second vessel = (1/6)x gallons

- Water in the first vessel = (1/9) * 26 gallons
- Water in the second vessel = (5/6)x gallons

The total milk and water in the third vessel should be equal, as the resulting mixture should be half milk and half water. Therefore, we can write the equation:

[(8/9) * 26] + [(1/6)x] = [(1/9) * 26] + [(5/6)x]

Simplifying the above equation, we get:

208/9 + (1/6)x = 26/9 + (5/6)x

Multiplying both sides of the equation by 54 to eliminate the denominators, we get:

624 + 9x = 156 + 45x

36x = 468

x = 468/36

x = 13

Therefore, 13 gallons of mixture should be drawn from the second vessel to fill the third vessel completely. Hence, option D is the correct answer.
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

Two vessels contain mixtures of milk and water in ratios 8 : 1 and 1 : 5, respectively. The contents of both of these are mixed in a specific ratio into a third vessel. How much mixture should be drawn from the second vessel to fill the third vessel (capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?a)12 gallonsb)14 gallonsc)10 gallonsd)13 gallonsCorrect answer is option 'B'. Can you explain this answer?
Question Description
Two vessels contain mixtures of milk and water in ratios 8 : 1 and 1 : 5, respectively. The contents of both of these are mixed in a specific ratio into a third vessel. How much mixture should be drawn from the second vessel to fill the third vessel (capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?a)12 gallonsb)14 gallonsc)10 gallonsd)13 gallonsCorrect answer is option 'B'. 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 Two vessels contain mixtures of milk and water in ratios 8 : 1 and 1 : 5, respectively. The contents of both of these are mixed in a specific ratio into a third vessel. How much mixture should be drawn from the second vessel to fill the third vessel (capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?a)12 gallonsb)14 gallonsc)10 gallonsd)13 gallonsCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two vessels contain mixtures of milk and water in ratios 8 : 1 and 1 : 5, respectively. The contents of both of these are mixed in a specific ratio into a third vessel. How much mixture should be drawn from the second vessel to fill the third vessel (capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?a)12 gallonsb)14 gallonsc)10 gallonsd)13 gallonsCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Two vessels contain mixtures of milk and water in ratios 8 : 1 and 1 : 5, respectively. The contents of both of these are mixed in a specific ratio into a third vessel. How much mixture should be drawn from the second vessel to fill the third vessel (capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?a)12 gallonsb)14 gallonsc)10 gallonsd)13 gallonsCorrect answer is option 'B'. Can you explain this answer? 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 Two vessels contain mixtures of milk and water in ratios 8 : 1 and 1 : 5, respectively. The contents of both of these are mixed in a specific ratio into a third vessel. How much mixture should be drawn from the second vessel to fill the third vessel (capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?a)12 gallonsb)14 gallonsc)10 gallonsd)13 gallonsCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Two vessels contain mixtures of milk and water in ratios 8 : 1 and 1 : 5, respectively. The contents of both of these are mixed in a specific ratio into a third vessel. How much mixture should be drawn from the second vessel to fill the third vessel (capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?a)12 gallonsb)14 gallonsc)10 gallonsd)13 gallonsCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Two vessels contain mixtures of milk and water in ratios 8 : 1 and 1 : 5, respectively. The contents of both of these are mixed in a specific ratio into a third vessel. How much mixture should be drawn from the second vessel to fill the third vessel (capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?a)12 gallonsb)14 gallonsc)10 gallonsd)13 gallonsCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Two vessels contain mixtures of milk and water in ratios 8 : 1 and 1 : 5, respectively. The contents of both of these are mixed in a specific ratio into a third vessel. How much mixture should be drawn from the second vessel to fill the third vessel (capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?a)12 gallonsb)14 gallonsc)10 gallonsd)13 gallonsCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Two vessels contain mixtures of milk and water in ratios 8 : 1 and 1 : 5, respectively. The contents of both of these are mixed in a specific ratio into a third vessel. How much mixture should be drawn from the second vessel to fill the third vessel (capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?a)12 gallonsb)14 gallonsc)10 gallonsd)13 gallonsCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
Explore Courses for CAT exam

Top Courses for CAT

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev