Proportion and Partnership

We need to compare the two quantities for many reasons. We compare them to find out which quantity is greater and smaller and the extent by which they are greater or smaller than each other. There are numerous ways to compare two quantities with each other.

Ratio and proportion are two of those ways. A ratio compares two quantities with the same units, and when two ratios are set equal to each other, they are said to be in proportion. Let us also take a look at the concept of partnership and various types of it.

Partnership

A partnership is when a minimum of two individuals join hands in order to achieve a common Objective. Each individual is required to contribute cash, time, or licenses in order to avail benefits from the association.

There are two types of partners, as stated below.

• Sleeping Partner: A sleeping partner’s only contribution is an investment of money. 

• Working Partner: A working partner is one who invests money as well as manages the business.

Partnership topic is related to the ratio topic proportion in the following ways:

• The investment by the individual and the benefit obtained is distributed among the individuals in proportion.
• When the investment periods end, the acquired profit or the incurred loss is in the ratio of the corresponding investments.

Types of Partnership

There are two types of partnership which are following:

• Simple Partnership: In a simple partnership, all the investors invest the resources for the same period. 

Hence, all the resources stay in business for the same amount of time.

• Compound Partnership: The type of partnership in which different investors invest the resources for a variable amount of time. In a compound partnership, the amount of benefit that each investor will be enjoying is evaluated by duplicating the money contributed with the unit of time.

Ratio and Proportion

Ratio and proportion are important concepts of mathematics that help in the comparison of two quantities. In the CLAT examination, ratio and proportion questions are asked because this concept has real-life applications. There is also the law of variable proportions. 

Ratio

The ratio is the mathematical term to compare two similar types of quantities with the same units. 

The ratio of the term x to the term y is denoted by x: y.

A ratio consists of two components:

• Antecedent: Antecedent is the numerator part of the ratio.

The Antecedent in the above ratio is the term x.

• Consequent: The consequent is the denominator part of the ratio.

In the above ratio, they are the consequent.

Multiplication and Division rules for Ratio

The following rules are important for ratios:

• If we multiplied the Antecedent and the consequent of the ratio by the same number at the same time, the ratio is not at all affected.

• Similarly, when we divide the numerator and the denominator of the ratio by the same number at the same time, then the ratio will remain the same.

Note that this number cannot be zero.

Comparison of Two Ratios

We can compare two quantities with each other with help or ratio and determine the smaller or greater one, but how do you compare two ratios with each other?

• First, you reduce the two ratios to fractions with a common denominator.
• Then you compare the numerators with each other.
• The ratio with the fraction having a greater numerator is considered to be greater.

Proportions

If two ratios are equal to each other, then the four quantities that compose the two ratios are said to be in proportion.

If a/b= c/d, then the quantities a, b, c, and d are said to be in proportion. 

This proportion is expressed in the following way:

a:b = c:d or a:b::c:d

For four quantities that are said to be in proportion, the product of two extreme quantities is equal to the product of two mean quantities.

For example: If a, b, c, and d are four quantities in proportion such that a/b = c/d, then the product of a and d is equal to the product of b and c.

i.e., a×d = b×c

Even three quantities can be in proportion. That type of proportion is called the continued proportion.

It is represented as:

a:b = b:c

The product of a and c is equal to the square of b.

Law of variable proportions

The law of the variable proportions determines how the output changes when you increase the number of units of the variable factor.

The law of readable proportions states that:

If the number of variable factors is increased by the producer while the other factors are kept the same, then the total product increases at first, then at a diminishing rate, and finally, the decline begins.

Conclusion

The concept of ratio, proportion, and partnership is important as these concepts allow us to compare two quantities and determine the greater or the smaller one.

A partnership is when two individuals join hands to work towards achieving a common objective. A partnership can be simple or compound. In ratio, We compared two quantities that have similar units. The ratio of quantity a and quantity b is represented as a: b. When two ratios are equal to each other, then the four quantities which make up the two ratios are said to be in proportion with each other.