

Direct Formula / Rule 25 :
Theorem:
One type of liquid contains x% of A, the other
contains y% of A. A can is filled with n parts of the first
liquid and m parts of the second liquid. Then the percentage
of liquid A in the new mixture is given by
= 
[ 
nx + my 
] 
percent. 
(n + m) 
Example :
One type of liquid contains 25% of milk, the other
contains 30% of milk. A can is filled with 6 parts of the
first liquid and 4 parts of the second liquid. Find the
percentage of milk in the new mixture.
Detail Method :
The reqd. percentage of milk in the new
mixture
= 
Quantity of milk in the new mixture 
X 100 
Quantity of the new mixture 
= 
6 parts of 25% milk + 4 parts of 30% milk 
X 100 
(6 parts + 4 parts)of the liquid 
= 
6 X 25/100 + 4 X 30/100 
X 100 
10 
= (15 + 12) = 27
Ailigation Method :
= 
30  x 
= 
6 
= 
3 
x  25  4  2 
or, 60  2x = 3x  75
or, 5x = 60 + 75
∴ x = 27%
Quicker Method : Here you can use direct formula :
required answer = 
6 X 25 + 4 X 30 
= 
270 
= 27%. 
6 + 4  10 
Exercise :

A solution of sugar syrup has 15% sugar. Another solution
has 5% sugar. How many litres of the second solution must be added to 20 litres of the first solution to
make a solution of 10% sugar?

One type of liquid contains 15% of milk, the other contains
20% of milk. A can is filled with 4 parts of the first
liquid and 11 parts of the second liquid. Find the percentage
of milk in the new mixture.

One type of liquid contains 12 1/2% of milk, the other
contains 15% of milk. A can is filled with 8 parts of the
first liquid and 12 parts of the second liquid. Find the
percentage of milk in the new mixture.
Answers :
1 = 20, 2 = 18 2/3%, 3 = 14%



