# IBPS Quantitative Aptitude Online Course Chapter 5

This is fifth chapter of IBPS Quantitative Aptitude Online course. If you have not read previous four chapters then it is better to read them first. Each chapter covers different topic. Below is link to fourth chapter.Ideally you should start with chapter 1.Chapter 4 has links to all previous chapters.

Chapter 4 – Click to read chapter 4

In this chapter we will cover Percentage, Average and Mixture and Allegations.These are important concepts.These concepts are mixed with other topics to create questions. Every year you will get decent number of questions on these two topics.

__Percentage__

Percentage is a representation of fraction whose denominator is always 100, for example if we say 5%, then in fraction it implies “5/100”=1/20. Again fraction is represented in percentage as 4/5×100=80%.

__Formula 1
__

Suppose price of commodity increases by X%, by what percentage consumption should decrease to keep expenditure intact?

For problems of this kind formula is [X/(100+X)] * 100

Formula 2

Suppose price of commodity decreases by X%, by what percentage consumption should increase to with expenditure unchanged?

For problems of this kind formula is [X/(100**–**X)] * 100

Formula 3

x% of y is equal to y% of x

Formula 4

If x is p% of y then y is (100*100*x) / p

Formula 5

If an item price is changed by a% and b% successively then net change is given by

(a+b+ ab/100)%

**Average**

You will not find problems based on averages only. But this concept is used along with other ones to create problems in competitive exams like IBPS.

Formula 1

Average = Sum of all quantities / number of quantities

Formula 2

Average speed = Distance / total time

Formula 3

If an object covers equal distances at x km/hr and y km/hr then

Average Speed = 2xy / (x+y)

**Mixture and Allegations**

Mixture and Allegations is very important concept. Yet there are only two types of problems you have in exams. I have mentioned both the formulas below. You need to understand the concept and remember the formula to solve the problems faster.

Formula 1

Quantity of cheaper / Quantity of dearer = (Cost price of dearer – mean price) / (mean price – cost of cheaper)

If cost price of cheaper item is c ,If cost price of dearer item is d and mean price is m then

cheaper quantity : dearer quantity = (d – m) : (m – c)

Formula 2

If a is original quantity and b is quantity that is replaced and n is number of times replacement process is carried out then

Quantity of original after n operation / Quantity of mixture = (a-b/a) to the power n

We will now move to Chapter 5 which will cover other topics important for the exams.

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