Question: Two vessels A and B contain spirit and water mixed in the ratio 5:2 and 7:6 respectively. Find the ratio in which this mixture be mixed to obtain a new mixture in vessel c containing spirit and water in the ratio 8:5?
- 1:7
- 2:9
- 3:8
- 7:9
- 8:9
Correct Answer: D
Solution and Explanation:
Approach Solution 1:
The problem statement states that:
Given:
- Two vessels A and B contain spirit and water mixed in the ratio of 5:2 and 7:6 respectively.
Find Out:
- The ratio in which this mixture is mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8:5.
A ratio reflects a part to part relation. In this case, we need to find out the ratio of spirit to water.
The total of one entity whose elements are reflected in a ratio is the sum of both these entities.
Volume of Spirit in Vessel A = 5/ (5+2) *x
=> Volume of Spirit in Vessel A = 5/7x……. (1)
Volume of Spirit in Vessel B = 7/ (7+6) *y
=> Volume of Spirit in Vessel B = 7/13y……. (2)
Volume of Spirit in Vessel C = 8/ (8+5) *[x+y]
=> Volume of Spirit in Vessel C = 8/13 [x+y]
To get the volume of spirit in vessel C we need to add the equations (1) and (2) –
Volume of Spirit in Vessel C = 5/7x + 7/13y
Therefore, we can say:
=> 8/13 [x+y] = 5/7x +7/13y
=> 8/13x + 8/13y = 5/7x +7/13 y
=> 8/13y – 7/13y = 5/7x – 8/13x
=> 1/13y = [65 – 56]/91x
=> 1/13y = 9/91x
=> y = 9/91x * 13
=> y = 9/7x
So, y/x = 9/7 and x/y = 7/9 or x : y = 7 : 9
The mixture in vessel A and B need to be mixed in the ratio of 7:9 to obtain a new mixture in vessel C containing spirit and water in the ratio of 8:5.
Approach Solution 2:
The problem statement informs that:
Given:
- Two vessels A and B contain spirit and water mixed in the ratio of 5:2 and 7:6 respectively.
Find Out:
- The ratio in which this mixture is mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8:5.
Vessel C contains a ratio of spirit and water being 8:5
This implies that the total volume of contents in the vessel is 8+5 = 13 units
The contents of vessel C are made up of mixing the contents from Vessel A & B.
Let’s assume that:
Contribution of vessel A = a litres
Contribution of vessel B = b litres
Total volume of vessel C’s contents = X litres
So, X = a + b ……. (1)
Therefore, the total volume of spirit in vessel C = 8/13X litres
Total Volume of Spirit that Vessel A contributed to Vessel C = 5/7a
Total Volume of Spirit that Vessel B contributed to Vessel C = 7/13b
Total Volume of Spirit in Vessel C = 8/13X
Now, total volume of spirit in Vessel C is equal to the sum of the spirit from Vessels A & B.
So, 8/13X = 5/7a + 7/13b
From Equation (1) we know that X = a + b
By plugging the value of X in the equation we get:
=> 8/13 [a+b] = 5/7a + 7/13b
=> 8/13a + 8/13b = 5/7a + 7/13b
=> 8/13b – 7/13b = 5/7a – 8/13a
=> 1/13b = [65 – 56]/91a
=> b = 9/91a * 13
=> b = 9/7a
=> b/a = 9/7 or a/b = 7/9.
So, a:b = 7:9
Hence, the mixture in vessel A and B need to be mixed in the ratio of 7:9 to obtain a new mixture in vessel C containing spirit and water in the ratio of 8:5.
Approach Solution 3:
The problem statement implies that:
Given:
- Two vessels A and B contain spirit and water mixed in the ratio of 5:2 and 7:6 respectively.
Find Out:
- The ratio in which this mixture is mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8:5.
Ratio of Spirit and Water in Vessel A = 5:2
So, Spirit in one Litre mix from Vessel A = 5/7 litre……(1)
Ratio of Spirit and Water in Vessel B = 7:6
So, Spirit in one Litre mix from Vessel B = 7/13 litre………(2)
Ratio of Spirit and Water in Vessel C = 8:5
So, Spirit in one litre mix from Vessel C = 8/13 litre ………..(3)
Using Alligation,
Therefore, A : B = 7 : 9
Hence, the mixture in vessel A and B need to be mixed in the ratio of 7:9 to obtain a new mixture in vessel C containing spirit and water in the ratio of 8:5.
“Two vessels A and B contain spirit and water mixed in the ratio 5:2”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. To solve the GMAT Problem Solving questions, the candidates must have a concrete knowledge of arithmetic, algebra and geometry. The candidates can analyse GMAT Quant practice papers to go through different types of questions that will enable them to improve their mathematical learning.
Suggested GMAT Problem Solving Questions
- A circle is inscribed in an equilateral triangle, Find area GMAT Problem Solving
- if a small juice can contain 200 milliliters of juice, how many liters GMAT Problem Solving
- Two trains, each 100 meters long take 60 seconds to cross each other GMAT Problem Solving
- To be considered for “movie of the year,” a film must appear in at lea GMAT Problem Solving
- What percent of a half dollar is a penny, a nickel, and a dime? (A pen GMAT Problem Solving
- If 10^50 – 74 is written as an integer in base 10 notation GMAT Problem Solving
- On dividing a number by 56, we get 29 as a remainder. GMAT Problem Solving
- The Product of Two Positive Numbers is 616. If the Ratio of the GMAT Problem Solving
- A Mixed Doubles Tennis Game is to be Played Between Two Teams. GMAT Problem Solving
- In the xy-Plane, a Line has Slope 3 and x-Intercept 3. GMAT Problem Solving
- The Greatest Common Divisor of Two Positive Integers is 25 GMAT Problem Solving
- A and B Working Separately Can Do a Piece of Work in 9 and 12 Days Respectively GMAT Problem Solving
- A Man Whose Bowling Average is 12.4 Takes 5 Wickets for 26 Runs GMAT Problem Solving
- 2^16 – 1 is Divisible by GMAT Problem Solving
- Which of the following equations has a root in common with x^2 - 6x +5=0 GMAT Problem Solving
- A plane traveling 600 miles per hour in 30 miles from Kennedy Airport GMAT Problem Solving
- Six men and fourteen women can complete a work in five days, whereas GMAT Problem Solving
- If x and k are integers and (12^x)(4^2x+1)= (2^k)(3^2) GMAT Problem Solving
- A milk vendor has 3 milk solutions at his disposal GMAT Problem Solving
- The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to GMAT Problem Solving
- In a triangle ABC, there are 5, 6, and 4 points, different from the ver GMAT Problem Solving
- Two pipes can fill a tank in 20 and 24 minutes respectively and a wast GMAT Problem Solving
- Which of the following is a factor of 18! + 1? GMAT Problem Solving
- Mrs. Sharma has a Few Chocolate Candies Which She Wants to Distribute GMAT Problem Solving
- The Value of a Car Depreciates at the Rate of 10% Per Annum GMAT Problem Solving
- A Train Travels from New York to Chicago, a Distance of Approximately GMAT Problem Solving
- The juice stall at the circus stocked just 2 brands of orang GMAT Problem Solving
- Alfa, Beta and Gamma are inner angles in a triangle. If Alfa = Beta + GMAT Problem Solving
- A sum of money is to be divided among Ann, Bob, and Chloe. First, Ann r GMAT Problem Solving
- Two Pipes Can Fill the Cistern in 10hr and 12 hr Respectively GMAT Problem Solving
- The Length of the Diagonal of Square S as well as the Lengths of the Diagonals GMAT Problem Solving
- Two Sides of a Triangle and their Included Angles are 4cm, 5cm and 30 GMAT Problem Solving
- How many even multiples of 9 are there from 1–1,000, inclusive? GMAT Problem Solving
- An industrial loom weaves 0.128 metres of cloth every second. Approxim GMAT Problem Solving
- Triangles ABC, ACD, and ABD are all isosceles triangles. Point E (not GMAT Problem Solving
- There are 3 Green Flags, 2 Red Flags and 3 Yellow Flags. If all the GMAT Problem Solving
- For a Certain Set of Numbers, If x is in the Set, Then Both –x^2 and −x^3 GMAT Problem Solving
- A Team Contributes Total of $399 From its Members GMAT Problem Solving
- Kali builds a tower using only red, green, and blue toy bric GMAT Problem Solving
- An art gallery owner is hanging paintings for a new show. Of the six GMAT Problem Solving
- The size of a television screen is given as the length of GMAT Problem Solving
- If w, x, y, and z are integers such that 1 < w < x < y < z GMAT Problem Solving
- Arjun and Bhim can run a full around a circular track in 4 minutes GMAT Problem Solving
- Joe drives 120 miles at 60 miles per hour, and then he drives GMAT Problem Solving
- What is the probability of getting two cards that belong to the same GMAT Problem Solving
- From the Even Numbers Between 1 and 9, Two Different Even Numbers GMAT Problem Solving
- When 20 is Divided by the Positive Integer k, the Remainder is k – 2. GMAT Problem Solving
- Three Workers, A, B, and C, can Complete a Certain Task GMAT Problem Solving
- A Certain Basket Contains 10 Apples, 7 of Which are Red and 3 are Green GMAT Problem Solving
- There are Five Bells Which Start Ringing Together at Intervals of 3, 6 GMAT Problem Solving
Comments