Alligation Method

Just like Algebraic method, Alligation Alternate Method can be used for calculating strength of a solution obtained by mixing 2 or more solutions of different strengths. It is a visual method for computing proportions

Steps:

  1. Make a tic-tac-toe grid.
  2. Enter the percentage strength of the higher strength solution in the upper left box.
  3. Enter the percentage strength of the lower strength solution in the lower left box.
  4. Enter the desired percentage strength in the center box.
  5. X is the unknown amount of higher strength solution to be mixed to obtain the desired strength.
  6. Y is the unknown amount of lower strength solution to be mixed to obtain the desired strength.
  7. Subtract B from C to solve for X.
  8. Subtract C from A to solve for Y.
  9. You will need X parts of A and Y parts of B to make X + Y parts of C.
  10. To convert parts to an actual volume amount, calculate as follows:

    $$ Volume \ of \ Solution \ A = { x \ part \over x + y \ parts} \times desired \ volume \ of \ Solution \ C $$

    $$ Volume \ of \ Solution \ B = { x \ part \over x + y \ parts} \times desired \ volume \ of \ Solution \ C $$

  11. Check your answer by adding the volume of solution A and the volume of solution B. The total should be the desired volume of solution C.

Let’s solve a problem using alligation method, which was solved earlier using the algebraic method.


Solved Problem: : In what proportions should 70 % dextrose and 10 % dextrose be mixed to make 1000 ml of 50 % dextrose?

Approach: set up a tic-tac-toe grid which includes the higher, lower and desired strengths.

$$ Volume \ of \ Solution \ A = {x \ part \over x \ + \ y \ parts } \times desired \ volume \ of \ solution \ C $$

$$ Volume \ of \ Solution \ A = {40 \ parts \over 20 + 40 \ parts } \times 1000 \ ml$$

$$ Volume \ of \ Solution \ A = 667 \ ml$$

$$ Volume \ of \ Solution \ B = {y \ part \over x + y \ parts } \times desired \ volume \ of \ solution \ C$$

$$ Volume \ of \ Solution \ B = {20 \ parts \over 20 + 40 \ parts} \times 1000 \ ml $$

$$ Volume \ of \ solution \ B = 333 \ ml $$

Answer: Mix 667 ml of 70 % dextrose solution with 333 ml of 10 % dextrose solution to obtain 1000 ml of 50 % dextrose solution.