# IBPS Quantitative Aptitude Online Course Chapter 3

This is third chapter of IBPS Quantitative Aptitude Online course. The first two chapters provided details about below topics

First Chapter – Number System , Powers and Surds

Second Chapter – Series , LCM and HCF

In this chapter we will cover Ratio Proportion and Time and Distance Chapters. These two chapters are very important from exam point of view. Every year you get questions from these two topics.

**Ratio and Proportion**

Formulae 1

If two ratios are equal they are said to be proportional.That is if

a / b = c / d the ac = bd.

Formulae 2

If a sum of money M is divided in the ratio a : b : c then the three parts are

First part = a*M / (a + b+ c)

Second part = b*M / (a + b+ c)

Third part = c*M / (a + b+ c)

Formulae 3

If a / b = c / d then (a+b) /(a-b) / (c+d)/(c-d)

Formulae 4

If ratio between first number and second number is a:b and ratio between second number and third number is c:d then ratio between first , second and third number will be ac:bc:bd .

Formulae 5

If a: b and b:c then b is called mean proportion of a and c. We have a*c= b* b that is product of a and c is equal to square of b

Formulae 6

If sides of a any two square or rectangle or circle (that is figures which have either length or width or radius) is in ratio a:b then there area will be in ratio a*a:b*b

Formulae 7

If sides of a any two cubes or cones or cylinders (that is figures which have length , width and height ) is in ratio a:b then there area will be in ratio a*a*a:b*b*b

Formulae 8

If investment is in ratio a:b and period of investment is in ratio c:d then ratio of profits is in ratio ac:bd

Formulae 9

If the ratio of two numbers is a:b and both number is increased by x and new ratio becomes c:d then

Sum of two numbers is x (a+b) (c-d) / (ad – bc)

Difference of two numbers is x (a-b)(c-d)/(ad-bc)

The first number is xa(c-d)/(ad-bc)

The second number is xb(c-d) / (ad-bc)

Formulae 10

If x kg of an item with price of a INR/kg is mixed with y kg of other item with price of b INR/kg then the price of mixture is given by (xa+yb)/(x+y)

**Time and Distance**

Formula 1

Speed = Distance / Time

Formula 2

The relative velocity of two bodies moving in same direction with velocity a and b is a – b (where a > b)

Formula 3

The relative velocity of two bodies moving in opposite direction with velocity a and b is a + b

Formula 4

If a body travels same distance d with speed a and b then average speed is

2ab / (a+b)

If a body travels for same time t with speed a and b then average speed is

(a+b)/2

Formula 5

A train or moving body should travel its own length plus length of stationary body like Bridge , Platform to pass the stationary body. The length of stationary body like man or pillar is not considered.

Formula 6

If a body changes its speed in ratio a:b then corresponding time ratio will be b:a

Formula 7

If a is velocity or speed of boat in still waters and b is velocity or speed of river or stream then

Velocity of boat downstream = a + b

Velocity of boat upstream = a – b

Speed of boat in still waters = (speed of boat in downstream + speed of boat in upstream) / 2

Speed of river = (speed of boat in downstream – speed of boat in upstream) / 2

This is end of third chapter we will cover more chapters in fourth chapter of the IBPS Quantitative Aptitude online course.

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