Question: A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture?

1. 17 : 3
2. 9 : 1
3. 3 : 17
4. 5 : 3
5. 11: 2

Correct Answer: B
Solution and Explanation:
Approach Solution 1:

The problem statement informs that:

Given:

• A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2.
• 10 litres of the mixture is removed and replaced with pure milk.
• The operation is repeated once more.

Find Out:

• The ratio of milk and water in the resultant mixture at the end of the two removals and replacement.

Total 20 Ltrs and ratio of milk and water = 3:2
Therefore, it implies 12 litres of milk and 8 litres of water.
Initially, the ratio of milk to water is 12 : 8
Removing half, we get = 6 : 4
Adding 10 litres of milk means 16 : 4
Removing half, we get = 8 : 2
Again, adding 10 litres of milk means 18 : 2
The ratio of milk and water in the resultant mixture at the end of the two removals and replacement.= 18 : 2 = 9:1

Approach Solution 2:

The problem statement states that:

Given:

• A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2.
• 10 litres of the mixture is removed and replaced with pure milk.
• The operation is repeated once more.

Find Out:

• The ratio of milk and water in the resultant mixture at the end of the two removals and replacement.

Total solution= 20 litres
Milk : water 3:2, then milk = 12 litres and water = 8 litres

As per the formula, Amount = Concentration * volume
Therefore, the concentration of water in the solution is:
8 = Cw * 20
Cw = 2/5

Step 1:

10 litres from 20 litres solution is removed.
In the leftover solution, the water concentration remains identical. i.e. 2/5.
The initial volume of the solution was 20, the new volume is 10 (after 10 litres is removed)

Step 2:

10 litres of pure milk is added to the solution, therefore the new solution is again 20 litres

As per the formula,
Initial Concentration (Ci) * Initial Volume (Vi) = Final Concentration (Cf) * final Volume (Vf)
(2/5) * 10 = Cf * 20
Cf = 2/5 (1/2)
The water amount will remain identical when initially in a 10-litre solution. However, the water concentration will change when milk is added to the initial 10-litre water

Step 3:
Now again from the Step 2 solution, a 10-litre solution is removed and 10-litre pure milk is added
cf = (2/5) (1/2) (1/2)
cf = 1/10 (this is a new concentration of Water in the solution)

Therefore the concentration of milk is 9/10
Hence, the ratio of milk : water is 9:1.

Approach Solution 3:

The problem statement declares that:

Given:

• A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2.
• 10 litres of the mixture is removed and replaced with pure milk.
• The operation is repeated once more.

Find Out:

• The ratio of milk and water in the resultant mixture at the end of the two removals and replacement.

Total solution= 20 litres
Milk : water 3:2, then water = 8 litres
Let Wo be the amount of water in the mixture with pure milk = 8 litres
Let Wr be the amount of water in the mixture after the replacement has taken place.
⇒Wr/Wo = (1− R/M)^n
Where R is the amount of mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated.

Hence, Wr/Wo = (1-10/20)^2 = (1/2)^2 = ¼
∴ Wr = Wo/4 = 8/4 = 2 litres
Hence, the mixture will have 18 litres of milk and 2 litres of water.
∴ the ratio of milk and water = 18 : 2 = 9 : 1

“A 20 litre mixture of milk and water contains milk and water”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “Foundations of GMAT Math”. The GMAT Problem Solving questions enhance the candidates’ skills in arithmetic, geometry and algebra. The candidates can go through GMAT Quant practice papers to improve their mathematical proficiency and knowledge.

Suggested GMAT Problem Solving Samples

• A certain computer program randomly generates equation of line is form GMAT Problem Solving
• A perfect number is one which is equal to the sum of all its positive GMAT Problem Solving
• At A Prestigious Dog Show, Six Dogs Of Different Breeds Are To Be GMAT Problem Solving
• The Average Wages of a Worker During a Fortnight Comprising 15 GMAT Problem Solving
• Which of the Following Fractions is the Largest? GMAT Problem Solving
• Alice and Bob Traveled in the Same Direction Along the Same Route at GMAT Problem Solving
• Paul, Quallis and Robert Divide a Sum of Money Among Themselves in the GMAT Problem Solving
• If A Sphere With Radius r Is Inscribed In A Cube With Edges Of Length GMAT Problem Solving
• A Globe Of Radius 8 Inches Is To Be Placed Into A Square Box For Shipment GMAT Problem Solving
• What is the sum of digits in decimal notation of number (10^20) - 16? GMAT Problem Solving
• Which of the following is equivalent to the pair of GMAT Problem Solving
• A password to a certain database consists of digits that can GMAT Problem Solving
• A Can do 1/3 of the Work in 5 Days and B Can do 2/5 of the Work in 10 Days GMAT Problem Solving
• The income of a broker remains unchanged though the rate of commission is increased GMAT Problem Solving
• Curly Brackets {} Around the Last Digits of a Decimal Fraction Signify GMAT Problem Solving
• For the infinite sequence a1, a2, a3, ... an, an+1, an=3(an−1) for all GMAT Problem Solving
• The quantities S and T are positive and are related by the equation GMAT Problem Solving
• A child paints the six faces of a cube with six different GMAT Problem Solving
• In an opera theater. there are 300 seats available GMAT Problem Solving
• At the Rate of m Meters Per s Seconds, How Many Meters Does a Cyclist GMAT Problem Solving
• NASA Received Three Messages in a Strange Language From a Distant Planet GMAT Problem Solving
• Two Cyclists Start From the Same Place to Ride in the Same Direction GMAT Problem Solving
• A Sphere is Inscribed in a Cube with an Edge of 10. What is GMAT Problem Solving
• If AC = BC and CD = DE Then, in Terms of x, the Value of y is GMAT Problem Solving
• What Is The Units Digit Of The Product Of Any Five Consecutive Positive Integers GMAT Problem Solving
• A Large Cube Consists Of 125 Identical Small Cubes GMAT Problem Solving
• A Pizzeria Makes Pizzas That Are Shaped As Perfect Circles GMAT Problem Solving
• The Number Of Diagonals Of A Polygon Of n Sides Is Given By The Formula GMAT Problem Solving
• The Work Done By A Woman In 8 Hours Is Equal To The Work Done By A Man GMAT Problem Solving
• A Circle Is Inscribed Inside Right Triangle Abc Shown Above GMAT Problem Solving
• The Temperatures In Degrees Celsius Recorded At 6 In The Morning In GMAT Problem Solving
• A Truck Travelling At 70 Kilometres Per Hour Uses 30% More Diesel To GMAT Problem Solving
• If The Area Of A Rectangle Is Equal To The Area Of A Square, Then The GMAT Problem Solving
• The rectangles shown above are similar and the ratio of the area of GMAT Problem Solving
• A School has Set Different Minimum Qualifying Marks in an Exam GMAT Problem Solving
• The Temperature of Delhi and Lucknow were in the Ratio 3:5 in July GMAT Problem Solving
• When a Certain Tree was First Planted, it was 4 feet Tall and the Height GMAT Problem Solving
• When a Number A is Divided by 6, the Remainder is 3 and When Another GMAT Problem Solving
• Which of the Following is the Correct Ordering of 2√13, 4√3, 5√2 and 3√6 ? GMAT Problem Solving
• If the mean of set S does not exceed mean of the subset of set S, which GMAT Problem Solving
• A Milkman Sells Milk after Adding Some Water in it GMAT Problem Solving
• It Was Observed by National Geographic that Equinox Happened GMAT Problem Solving
• Paracelsus University has Two Kinds of Professors, Academic Professors GMAT Problem Solving
• What is the Smallest Prime Factor of 5^8+10^6–50^3? GMAT Problem Solving
• In A Locality, There Are Ten Houses In A Row. On A Particular Night GMAT Problem Solving
• The “Connection” Between Any Two Positive Integers a And b GMAT Problem Solving
• Find the least positive integers which must be added to 15,463 so that the result GMAT Problem Solving
• Mayank Buys Some Candies for $15 a dozen and An Equal Number of Different GMAT Problem Solving
• If John Throws a Coin Until a Series of Three Consecutive Heads GMAT Problem Solving
• In the Diagram Above, ABCD is a Parallelogram and the Areas of Yellow GMAT Problem Solving