23. A vessel
is filled with liquid,3 parts of which are water and 5 parts syrup. How much of
the mixture must be drawn off and replaced with water so that the mixture may
be half water and half syrup?
Solution:
Suppose
the vessal initially contains 8 liters of liquid.
Let
x liters of this liquid be replaced with water
then
quantity of water in new mixture
=
3-(3x/8)+x liters.
Quantity
of syrup in new mixture = 5 - 5x/8 liters.
Therefore
3 - 3x/8 +x = 5 - 5x/8
5x+24
= 40-5x
10x
= 16.
x=
8/5.
So
part of the mixture replaced = 8/5*1/8 =1/5.
