# Alligation or Mixture

• It is a rule to find respective prices should be mixed to give a mixture at a given price.
• The means or average price of a mixture when the price of two or more ingredients which may be mixed together and the proportion in which they are mixed are given,
• Here, cost price of a unit quantity of mixture is called the mean price.
• Or in easy term Alligation is a rule which is used to solve the problems related to mixture and its ingredient.

Alligation Rule: Suppose, Rs. D per unit be the price of first ingredient (superior quality) mixed with another ingredient (cheaper quality) of price Rs.C per unit to form a mixture whose mean price is Rs.M per unit, then the two ingredients must be mixed in the ratio:

i.e. the two ingredients are to be mixed in the inverse ration of the two different are to be mixed and the mean price. The above rule may be represented schematically as under:

Explanation:

• Suppose x kg of cheaper quality is mixed with y kg of superior quality.
• Price of the cheaper ingredient – Rs.cx Price of superior ingredient = Rs.dy
• Price of mixture = Rs.(cx + dy)
• And quantity of mixture = (x + Y) kg.
• Price of mixture/kg = Rs. (cx + dy)
• and quantity of mixture = (x + y) kg.
• Price of mixture/kg = Rs. (cx+dyx+y)(cx+dyx+y)
• (cx+dyx+y)∴(cx+dyx+y) = m
• cx = dy = mx = my
• dy – my = mx – cx
• y(d – m) = x(m – c)
• xy=d−mm−c