# Percentages Part 8

Milk and water concept

Problem 1: A mixture of 40 lit of milk and water contains 10% water. How much water should be added so water may 20% in the mixture

Solution: Quantity of mixture  = 40 lit.

Percentage of water = 10%

The quantity of water = $\frac{40\times&space;10}{100}=4$ lit

The quantity of milk = 40-4=36

How much water should be added so water maybe 20% in the new mixture

$\frac{4+x}{36}=\frac{20}{80}$

x=5

Shortcut :

Water                      Milk                     Water                      Milk

10             :                90          $\rightarrow$             1               :               9

20             :                80         $\rightarrow$              1              :                4

To equate the milk multiply (1:9) with 4 and (1:4) with 9

Water                      Milk                                    Water                      Milk

( 1               :               9 )  *4          $\rightarrow$                      4               :              36

( 1               :               4 )  *9          $\rightarrow$                       9              :              36

4-9=5

$\rightarrow$  40

40 $\rightarrow$  ?     (36+4=40)

$\frac{5\times&space;40}{40}=5lit$

Problem 2: Fresh fruit contains 68% water and dry fruit contains 20% water. How many kgs of dry fruits can be made from 75kg of fresh fruit?

Solution :

Water                 pulp                               Water                 pulp

Fresh              68%          :         32%            $\rightarrow$                17           :             8

Dry                    20%          :        80%            $\rightarrow$                  2          :               8

17+8=25             2+8=10

25%  $\rightarrow$  75

10%  $\rightarrow$  ?

$\frac{10\times&space;75}{25}=30$

Problem 3: A solution of salt water contains 20% salt by weight. If 20lit of water is evaporated from the solution, the solution contains 25% of salt. What is the original quantity of solution?

Solution:

Salt                     Water                   Salt                     Water

20%       :             80%        $\rightarrow$             1           :               4

25%      :              75%        $\rightarrow$              1           :              3

1+4=5          1+3=4

5-4=1

$\rightarrow$  20lit

$\rightarrow$  ?

$\frac{5\times&space;20}{1}=100$