Question: To 100 litres of milk, 10 litres of water is added and then 20 litres of solution is removed. Next 30 litres of the water is added and 20 litres of solution is removed. What is the amount of milk, in litres, in the solution now?
- 720/11 litres
- 730/11 litres
- 740/11 litres
- 750/11 litres
- 760/11 litres
“To 100 litres of milk, 10 litres of water is added and then 20 litres”- is a topic of GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.
The candidate must have adequate qualitative skills in order to crack GMAT Problem-Solving questions. GMAT quant helps the candidates to measure their rational skills in maths concepts. The candidate must estimate logically to determine the correct choice. The GMAT Quant topic in the problem-solving part needs calculative mathematical problems that can be deciphered with good mathematical understanding.
Solution and Explanation:
Approach Solution 1:
The problem statement states that:
Given:
- 10 litres of water is added to 100 litres of milk.
- 20 litres of the solution is removed from the mixture.
- Then, 30 litres of water is added and 20 litres of the solution is further removed.
Find out:
- What is the final amount of milk in the solution?
Since 10 litres of water is added to 100 litres of milk, the amount of solution= 110 lt
The concentration of milk in this solution is therefore 100/110 = 10/11
Let the final concentration of milk be Cf and the initial concentration of milk be Ci
Assume the initial volume of solution is Vi and the final volume of milk is Vf.
20 litres in removed and 30 litres is added, therefore, Vi = 110-20 = 90 and Vf= 90 + 30= 120
Substituting all the values in the equation, it can be implied that
Cf = Ci * (Vi/ Vf)
Cf = (10/11) * (90/120)
= 30/44
This is the final concentration of milk in 120 litres of solution. Now again 20 litres is removed from the final solution.
Therefore, the volume of solution after removing 20lts = 120 - 20 = 100 litres
Amount of milt present in the solution = 100 * (30/44) = 750/11 litres
Hence, option D is the correct answer.
Approach Solution 2:
According to the problem statement,
Given:
- In 100 litres of milk, 10 litres of water is added.
- 20 litres of the solution is then removed from the mixture.
- Next, 30 litres of water is further added.
- 20 litres of the solution is again removed.
Find out:
- Find the final amount of milk in the solution.
100 litres of milk + 10 litres of water = 110 litres of solution
100/110 = 10/11 of 1 litre solution is milk.
20 litres of the solution is removed from the mixture.
(10/11)*20 = (200/11) litres of milk is removed from the mixture
Milk left= 100 - 200/11 = (900/11) litres
Then, 90 litres of solution = 30 litres of water = 120 litres solution
20 litres of the solution is further removed from 120 litres of the solution
In the 120 litres solution:
900/(11*120) = 90/132
90/132 of 1 litre solution is the quantity of milk
20* 90/132 = 1800/132 = (150/11)
(150/11) litres of 20 litres solution is the amount of milk
Therefore the amount of milk left in the solution = 900/11 - 150/11 = 750/11 litres
Hence, option D is the correct answer.
Approach Solution 3:
The problem statement implies that 10 litres of water is added to 100 litres of milk. Then 20 litres of the solution is removed. 30 litres of water is added again to the solution. 20 litres is further removed from the solution. Find the amount of milk present in the solution.
After 10 litres of water is mixed with 100 litres of milk, it will become a 110 litre solution.
The ratio of milk and water in the solution is 10:1.
After 20 litres of the solution is removed, the amount of solution left= 90 litres.
Since the ratio of milk and water at this point is still the same 10:1, the equation will be:
10x + x = 90
11x= 90
x= 90/11
Therefore, 90 litres of solution contains 900/11 litres of milk and 90/11 litres of water.
After 30 litres of water are mixed with the 90 litres of solution, the quantity of solution becomes = 120 litres.
In this 120 litres of solution, the amount of milk is 900/11 litres and the amount of water is 90/11 + 30
= 90/11 + 330/11
=420/11.
Therefore, the ratio of milk and water is 900/11: 420/11 = 900:420 = 15:7
20 litres of the solution is further removed.
The final quantity of solution is therefore= 100 litres.
Since the ratio of milk and water at this point remains the same at 15:7, the equation will be:
15y + 7y = 100
22y = 100
y= 100/22 = 50/11
Therefore, in 100-litre solution, the amount of milk is 15(50/11) =750/11 litres and amount of water= 7(50/11) = 350/11 litres.
Hence, option D is the correct answer.
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