Ratio, proportion, and allegation are among the most typical and tricky topic in the SSC exams. The difficulty level of questions varies from exam to exam. You will get tricky questions in SSC CGL, while in SSC CHSL & others questions remain simple. There will be 1-2 questions asked in tier-1 exams conducted by SSC. To solve such questions, you need to be very attentive in understanding the stated problem and the concept to derive the solution.

In this article, we will discuss about the tips and methods to solve the questions hailed from ratio, proportion, and allegation topic. Let us go through them-

**SSC Quantitative Aptitude tips: Ratio**

The ratio is the relationship in which one quantity is compared with another of the same kind. The ratio of two quantities, a and b is the fraction of a/b and we write it as a: b. In ratio a: b, we call a as the first term or **antecedent **and b, the second term or **consequent.**

**Note:** if each term of a ratio is divided or multiplied by the same non- zero number, then it does not affect the ratio.

Different types of ratio:- There are six types of ratios.

**Compound ratio:**- It is obtained by multiplying the numerators and denominators together. The compound ration of a : b and c:d is ac : bd.**Duplicate ratio:**-if x and y are the two numbers, then duplicate ratio between them will be x^{2}:y^{2}.**Sub-duplicate ratio:-**if x and y are the two numbers, then sub-duplicate ratio between them will be x^{1/2}:y^{1/2}.**Triplicate ratio:**- if x and y are the two numbers, then triplicate ratio between them will be x^{3}:y^{3}.**Sub-triplicate ratio:-**if x and y are the two numbers, then sub-triplicate ratio between them will be x^{1/3}:y^{1/3}.**Inverse ratio:**- this is obtained, when antecedent and consequent are mutually replaced by each other. The inverse ratio of a:b will be b:a.

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

**Example2. **If we divide 495 into two parts such that they are in the ratio of 7 : 2, then, find the values of both the parts?

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

Then, 7x+2x= 495; => x= 55;

So, the 1^{st} part = 7 ×55=385;

The 2^{nd} part = 2 ×55=110;

**Note:**

If the ratio of first, second, and third quantities is given by, ac : bc : bd. then, the ratio between first and second quantity will be a:b and third and fourth will be c:d.

Similarly, the ratio of first, second, third and fourth quantities is given by ace : bce : bde : bdf, then the ratio between first and second quantity will be a: b, second and third will be c :d and third and fourth will be e:f.

**SSC Quantitative Aptitude tips: Proportion**

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 the 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: If 5 pens cost Rs 10, then 15 pen cost?**

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

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

Required cost= product of means/ 5;

= 150/5= 30 Rs.

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

**Example: If 10 men can do a work in 20 days, then in how many days 20 men will take to do that work?**

**Sol:** 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

Similarly, required days= 200/20=10 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,

**SSC Quantitative Aptitude tips: Allegation**

The word allegation means linking. This is used to find, when any of the following is given:

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:** **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?**

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 qualities should be mixed in 39: 20: 20 ratios to have a new mixture of rice.

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