10 liters of milk is mixed with 5 liters of mixture of milk and water. if the final mixture has 12 liters of milk what is the percentage of water in the mixture?
Answers
Step-by-step explanation:
The concentration of initial mixture ={10/(10+40)}*100=20%The quantity of mixture is (10+40)litres=50 litres. The final concentration to remain 40%=>The milk quantity to be in the solution=50x40%=20litres.Let the pure milk to be added=X litres with replacing X litres of ex-mixture to make the mixture contain 20 litre of milk.X litre of ex mixture contain 20%ofx milk=0.2X.After taking away X litre from the ex-mixture+> it contains (10–0.2X) litres of milk.After adding X litres of pure milk=> the milk quantity in the new solution =10–0.2X+X=10+0.8X.Now 10+0.8X=20=>0.8X+10=>X =10/0.8 .So 12.5litres of old solution to be replaced with pure milk.
Answer:
Initially 5% is the portion of the water in the mixture, 95% is the portion of the milk in the mixture.
So quantity of water(in litres) in the 10 litres =
100
5
×10 litres =0.5 litres
And also quantity of milk in 10 L mixture =
100
95
×10 L =9.5 L
Let X be the quantity of pure milk to be added to the mixture to make water content to 2%.
∴
(9.5+x)
0.5
×100=
9.8
0.2
×100
⇒9.8×0.5=0.2(9.5+x)
⇒4.9=1.9+0.2x
⇒0.2x=3.0
⇒x=15
So, 15 liters of pure milk should be added to the mixture to reduce the water content to 2%