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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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