How much pure alcohol has to be added to 400ml of a solution containing 15% alcohol to change the concentration of alcohol in the mixture to 32%?
if x ml of 100% alcohol are added, then you want
.15(400) + 1.00x = .32(400+x)
Qus-a sum of 500 Rs is in the form of denominations of 5 and 10 if the total numder of notes is 90 find the number of notes of each type
solve- lets 5Rs notes =x
10 Rs notes =(90-x)
Atoq
5¡Áx+10¡Á(90-x)=500
5x+900_10x=500
-5x=500-900
-5x=-400
5x=400
X=400/5
x=80
Number of 5 Rs notes =80
Number of 10 Rs nots=(90-x)
=(90-80)=10 ANSWER
To determine how much pure alcohol needs to be added to change the concentration of alcohol in the mixture, we can set up a simple equation using the concept of the amount of alcohol.
Let's break down the problem step by step:
Step 1: Calculate the amount of alcohol in the original solution.
The original solution has a volume of 400ml and contains 15% alcohol.
So, the amount of alcohol in the original solution is (15/100) * 400ml = 60ml.
Step 2: Calculate the final volume of the solution.
We are adding pure alcohol, which means the final volume will be the sum of the original 400ml and the amount of pure alcohol added. Let's call the amount of pure alcohol added "x". So, the final volume will be 400ml + x.
Step 3: Calculate the amount of alcohol in the final solution.
Since we are aiming for a 32% concentration, the amount of alcohol in the final solution will be (32/100) * (400+x) ml.
Step 4: Set up the equation.
According to the law of conservation of mass, the amount of alcohol before and after the addition should be the same. Therefore, we can set up the equation:
Amount of alcohol in the original solution = Amount of alcohol in the final solution.
60ml = (32/100) * (400+x) ml.
Step 5: Solve for "x".
Let's solve the equation:
60 = (32/100) * (400 + x).
To simplify, let's multiply both sides by 100 and divide by 32:
6000 = 400 + x.
Now, isolate the "x" term by subtracting 400 from both sides:
x = 6000 - 400.
x = 5600 ml.
Therefore, you need to add 5600 ml of pure alcohol to the 400 ml of the 15% alcohol solution to change the concentration to 32%.