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17 Dec 2024, 00:55
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
77% (01:45) correct
23%
(01:51)
wrong
based on 178
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10% of milk and water solution with 40% milk is replaced with water. What is concentration of milk in the resultant solution?
A. 20%
B. 32%
C. 18%
D. 40%
E. 36%
A. 20%
B. 32%
C. 18%
D. 40%
E. 36%
19 Dec 2024, 23:31
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Equate water quantity in initial and final solution.
Let total quantity of initial solution be T, then quantity of water would be 60% ie, 3T/5.
Let x be the quantity of solution replaced with water ie. x = 10% of T = 0.1T.
Quantity of water in the final solution = Quantity of water in the initial solution after x quantity is removed + Quantity of water added
= (T - x)(3/5) + x = \( \frac{(T - 0.1T)*3}{5}\) + 0.1T = \(\frac{(2.7T + 0.5T)}{5}\) = \(\frac{32T}{50}\) = \(\frac{64T}{100}\)
Percentage of water in final solution = (100*Quantity of water)/Total quantity = \(\frac{100*(64T/100)}{T}\) = 64%
Percentage of milk = 100 - Percentage of water = 100 - 64 = 36
Answer: E
Let total quantity of initial solution be T, then quantity of water would be 60% ie, 3T/5.
Let x be the quantity of solution replaced with water ie. x = 10% of T = 0.1T.
Quantity of water in the final solution = Quantity of water in the initial solution after x quantity is removed + Quantity of water added
= (T - x)(3/5) + x = \( \frac{(T - 0.1T)*3}{5}\) + 0.1T = \(\frac{(2.7T + 0.5T)}{5}\) = \(\frac{32T}{50}\) = \(\frac{64T}{100}\)
Percentage of water in final solution = (100*Quantity of water)/Total quantity = \(\frac{100*(64T/100)}{T}\) = 64%
Percentage of milk = 100 - Percentage of water = 100 - 64 = 36
Answer: E
20 Dec 2024, 10:28
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MalachiKeti
We need to calculate the concentration of milk in the solution after 10% of it is replaced with water when the initial solution contains 40% milk. Here's a step-by-step explanation:
Step 1: Understand the problem.
- Initial concentration of milk: 40%.
- Replacement process: 10% of the solution is replaced with water.
- This process reduces the milk concentration since pure water (0% milk) is added.
Step 2: Define the key formula.
Each time we replace a fraction of the solution with water, the new concentration of milk can be calculated using the formula:
Cnew=Cold×(1−r)
Where:
- Cnew = new concentration of milk.
- Cold = old concentration of milk.
- r = fraction of solution replaced with water (10% = 0.1).
Step 3: Perform the calculations.
- First replacement:
Cnew=40%×(1−0.1)=40%×0.9=36%
Thus, after the replacement, the concentration of milk in the resultant solution is 36%.
Final Answer:
The concentration of milk in the resultant solution is 36%, which corresponds to Option E.
