Word Problem 17 (Partial percentage, mixture)
Problem 17 : A mixture of 70 liters of milk and water contains 10% water. How much water must be added to make water 12-1/2 % ?
a) 10 b) 5 c) 2 d) 12
Solution:
Let y liters of water be added to make water 12.5 %
\[ Then Quantity Of Water = (7+y) Liters \]
And
\[ Quantity Of Mixture = (70+y) Liters \]
New concentration of water in the mixture can be expressed as ;
\[ New Concentration = \frac{water}{Mixture}\times 100 \]
This gives;
\[ y+7 = \frac{12.5} {100} \times70 \]
So we get;
\[ 12.5(70+y)=(7+y) \times100 \]
or
\[ 875+12.5y=700+100y \]
or
\[ 875-700=100y-12.5y \]
or
\[ 175=87.5y \]
or
\[ y= \frac {175}{87.5}=2 Liters \]
So, two liters of water should be added to make concentration of water to be 12-1/2% or 12.5 %
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