Partnership, Mixture and Alligations

In business math, it’s important to know about partnership, mixture and alligations. The topic is under arithmetic and here we will discuss about the important facts and formulas.

Partnership is an important deal when two or more than two persons invest or run a business jointly, they are called partners. If in a partnership

business the investments are made by the 1st, 2nd and the 3rd partners are x1, x2, x3 respectively, the time period be t1, t2, t3 then the ratio of profits is given by x1 t1 : x2 t2 : x3 t3.

If x1 : x2 : x3 is the ratio of investments and p1 : p2 : p3 be the ratio of profits, the ratio of time periods is given by p1/x1 : p2/x2 : p3/x3

If p1 : p2 : p3 is the ratio of profits and t1 : t2 : t3 be the ratio of time periods, the ratio of investments is given by p1/t1 : p2/t2 : p3/t3

Alligation is the rule that help us to find the required mixture of a desired price when two or more ingredients are mixed in a definite ratio at the given price

Mean price is the cost price of a unit quantity of the mixture.

Rules of Alligation

Suppose two ingredients are mixed at the given prices are known, then the ratio in which these two are mixed to obtain a mixture of a known price is given by

Quantity of cheaper

__________________ =

Quantity of dearer

Cost price of dearer - Mean Price


Mean price - Cost price of cheaper

The above relationship can also be represented as under:

Partnership, Mixture and Alligations

Hence, (cheaper quantity) : (dearer quantity) = (d - m) : (m - c)

Suppose a container contains x units of liquids from which y units of liquids is taken out, and is replaced with y units of water, the process being repeated n times, then the final quantity of the liquid in the container is given by

x(1 - y/x)n units.

These are the important facts and formulas about the partnership, mixture and alligations to solve the related problems.

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