Staff Selection Commission conducts Combined Graduate Level Exam for the recruitment to the different Group ‘B’ and Group ‘C’ posts. Jagranjosh.com has come up with SSC CGL Exam (Tier-I): Reasoning: Ratio and Proportion: Concepts & Free Online Practice Set. Here, we provide concepts along with Free Online Practice Set to make the ease of students in cracking Ratio and Proportion questions in exam.

**Ratio**

**Introduction:**

Ratio is the relation which one quantity bears to another of the same kind. The ratio of two quantities a and b is the fraction a/b and we write it as a: b.

In the ratio a: b, we call a as the first term or **antecedent **and b, the second term or **consequent.**

**Note:** The multiplication or division of each term of a ratio by the same non- zero number does not affect the ratio.

**Compound Ratio:** - It is obtained by multiplying together the numerators for new numerator and denominators for new denominator.

**Example 1. **If the ratios are 4:3, 15:20, 2:6 and 3:5 find the compound ratio?

**Example2. **If we divide 4185 into two parts such that they are in ratio 7:2, then find the values of both the parts?

Sol 2. Let the actual variable be 7x and 2x.

So, the 1^{st} part = 7 ×465=3255

The 2^{nd} part = 2 ×465=930

**Note:**

The ratio of first , second and third quantities is given by

ac : bc : bd

If the ratio between first and second quantity is a:b and third and fourth is c:d .

Similarly, the ratio of first, second, third and fourth quantities is given by

ace : bce : bde : bdf

If the ratio between first and second quantity is a: b and third and fourth is c:d.

** Proportion****Introduction:-**

Four quantities are said to be proportional if the two ratios are equal i.e. the A, B, C and D are proportion. It is denoted by “::” it is written as A : B : C : D where A and D are extremes and B and C are called means .** Product of the extreme = Product of the means****Direct proportion:** - The two given quantities are so related that if one quantity increases (or decreases) then the other quantity also increases (or decreases).

Example 1. If 5 pens cost Rs 10 then 15 pen cost?

Sol 1. It is seen that if number of pens increases then cost also increases. So,

5 pens: 15 pens:: Rs 10 : required cost

**Inverse proportion:** - The two given quantities are so related that if one quantity increases (or decreases) then the other quantity also decreases (or increases).

Example 2.If 10 men can do a work in 20 days then in how many days 20 men can do that work?

Sol 2. Here if men increase then days should decrease, so this is a case of inverse proportion, so

10 men: 20 men :: required days : 20 days

**Rule of three:** It Is the method of finding 4th term of a proportion if all the other three are given, if ratio is a:b :: c:d then ,

** ALLIGATIONIntroduction:-**

The word allegation means linking. It is used to find:

1. The proportion in which the ingredients of given price are mixed to produce a new mixture at a given price.

2. The mean or average value of mixture when the price of the two or more ingredients and the proportion in which they are mixed are given.

**Mathematical Formula:**

**For two ingredient:-**

**Example 1:** If the rice at Rs 3.20 per kg and the rice at Rs 3.50 per kg be mixed then what should be their proportion so that the new mixture be worth Rs 3.35 per kg ?

**Sol 1: **CP of 1 kg of cheaper rice CP of 1 kg of dearer rice

Hence they must be mixed in equal proportion i.e. 1:1

**Example 2:** Find out the ratio of new mixture so that it will cost Rs 1.40 per kg from the given three kinds of rice costing Rs 1.20, Rs 1.45 and Rs 1.74?

**Sol 2:** 1^{st} rice cost = 120, 2^{nd} rice cost = 145 and 3^{rd} rice cost = 174 paisa.

From the above rule: we have,

Therefore, three rice must be mixed in 39: 20: 20 ratios to have a new mixture of rice.