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Quantitative Aptitude – Area

One of the most important chapter on quantitative aptitude is Area. Most of the competitive exams, which have quantitative aptitude part, have questions from area chapter. So, learn this topic very carefully.

In quantitative aptitude part of your exam, few question will surely come from area chapter. To solve those questions, you need to learn area chapter very carefully. Now here in this page below we discuss the basic ideas and formulas of area chapter. Read carefully are practice the practice set to improve your learning skills.

What is Area ?

In mathematical term we can define area as a amount of two dimensional space which is acquire by an object.

 

Basic formulas of Area
Rectangle

• 1. Areα of a Rectangle = (Length x Breadth)
  therefore, Length = (Areα / Breadth) and Breadth = (Areα / Length).

• 2. Perimeter of a Rectangle = 2 x (Length + Breadth).

Square

• Areα of a Square = (side)² = ½(diagonal)².

Triangle

• Areα of a Triangle = ½ x Base x Height.

• Areα of a Triangle = √(s(s-x)(s-y)(s-z)).
  where x, y, z are the sides of the triangle and s = ½(x + y + z).

• Areα of an equilateral Triangle = √¾ x (side)².

• Radius of incircle of an Equilateral Triangle of side x = x / (2√3).

• Radius of circumcircle of an Equilateral Triangle of side x = x / √3.

• Radius of incircle of a Triangle of areα Δ and semi-perimeter r = Δ / s.

Circle

• Areα of a circle = ΠR², where R is the radius.

• Circumference of a circle = 2ΠR.

• Length of an arc = 2ΠRθ / 360, where θ is the central angle.

• Areα of a sector = ½(arc x R) = ΠR²θ / 360.

Semi-Circle

• Circumference of a semi-circle = ΠR.

• Areα of semi-circle = ΠR² /2.

Parallelogram

• Areα of Parallelogram = (Base x Height).

Rhombus

• Areα of a Rhombus = ½ x (Product of diagonals).

Trapezium

• Areα of a trapezium = ½ x (sum of parallel sides) x distance between them.

Others

• Areα of four walls of a room = 2 (Length + Breadth) x Height.

 

So, this is the basic idea and formulas of this topic. Now, if you have any query or question to ask, then please feel free to ask us here. Our team members of www.AptitudeTricks.com will discuss about your questions.

Quantitative Aptitude – Volume and Surface Area

In quantitative aptitude, one of the most important topic is “Volume and Surface Area”. This chapter is one of the important topic in competitive exams. Few questions will surely come from this topic.

So, you need to prepare this chapter very carefully. Learn the basic idea and basic formulas of Volume and Surface area. This will help you to solve the questions of volume and surface area in your exams.

Now, we will discuss the details of basic idea and formulas of this topic. Let’s starts-

What is Volume and Surface Area ?

Definition: Using Volume and Surface area we can measure the size of an object, specifically a 3D object.

So, basically we use this formulas to find out the size of 3D objects like, Cube, Cuboid, Cone, Cylinder, Sphere, Hemisphere etc.

Questions of this types are most common in competitive exams. To solve those questions, you need to learn the formulas of this topic. So, let’s explain the formulas of Volume and Surface area.

 

Formulas of Volume and Surface Area

Cube

Let the length of each edge of a Cube is x. Then,

A. Volume = x³ cubic units.

B. Surface area = 6x² square units.

C. Diagonal = √3x units.

 

Cuboid

Let length = l, breadth = b and height = h units. Then

A. Volume = (l x b x h) cubic units.

B. Surface area = 2(lb + bh + lh) square units.

C. Diagonal = √(l² + b² + h²) units.

 

Cylinder

Let Height or length = l and radius of base = r. then,

A. Volume = (Πr²l) cubic units.

B. Curved surface area = (2Πrl) square units.

C. Total surface area = 2Πr(l + r) square units.

 

Cone

Let radius of base = r and Height = h. then,

A. Slant height, l = √(h² + r²) units.

B. Volume = 1/3Πr²h cubic units.

C. Curved surface area = (Πrl) square units.

D. Total surface area = (Πrl + Πr²) square units.

 

Sphere

Let the radius of the sphere = r. then,

A. Volume = 4/3Πr³ cubic units.

B. Surface area = 4Πr² square units.

 

Hemisphere

Let the radius of a hemisphere = r. then,

A. Volume = 2/3Πr³ cubic units.

B. Curved surface area = (2Πr²) sq. units.

C. Total surface area = (3Πr²) sq. units.

Note: 1 liter = 1000 cm³.

 

So, this is the basic idea and basic formulas of Volume and Surface chapter. Now, if you have any questions or doubts in your mind, then please feel free to ask us here in www.AptitudeTricks.com. Our team member will answer your questions and clear your doubts.

Quantitative Aptitude – Compound Interest

Preparation for competitive exam will not completed without the learning of Compound Interest. Questions from this chapter is often come in every competitive exams. So it’s a very important chapter to learn.

Learning process of Compound interest is not a very difficult job. It takes few minutes and good concentration to learn. So, concentrate and practice more to become an expert. Now we will discuss basic concept and formulas of Compound interest.

What is Interest ?

Money is not free to borrow. So, when we borrow some money from someone we need to pay some extra money to use the actual money. That extra money is called Interest.

Interest is basically calculate as a percentage on actual borrowed money per year. This means interest will be charged on the money every year at a percentage.

Suppose, Mr. Kumar borrow Rs.20000/- from a bank. He will use that money for 1 year. Now bank charges 10% interest rates on borrowed money. So, how much money Mr. Kumar will pay to the bank after 1 year.

Bank charge in one year is-

20000 X 10% = 2000

So, After one year Mr. Kumar needs to pay the actual amount plus the borrowed fees charged by bank. That is –

20000 + 2000 = 22000

So, Mr. Kumar will pay total Rs.22000/- after one year.

 

Types of Interest

Interest is basically of two types-

• Simple Interest
• Compound Interest

Now here in this page we will discuss Compound Interest. If you want to know more about Simple Interest then please Click Here.

 

What is Compound Interest ?

Definition: When the interest of borrowed money is calculated uniformly for a certain period of time, then the interest is called Compound Interest.

Suppose Mr. Kumar borrowed Rs.20000/- from a bank for 3 years at 10% interest rate. Now if bank chargers compound interest on borrowed money, then Mr. Kumar needs to pay-

Charges for 1st year:

20000 X 10% = 2000

Charges for 2nd year:

20000 X 10% = 2000

Charges for 3rd year:

20000 X 10% = 2000

So, if bank charges 10% interest rates uniformly for 3 years on Rs.20000/-, then Mr Kumar needs to pay Rs.6000/- as interest and total Rs.26000/- after 3 years.

 

Important Formulas

Before discussing the formulas of this topic, you should know few basic terms of interests.

• Borrowed Money = Principal = P
• Rate of Interest = R
• Time = T

Formulas:

• Compound Interest (C.I.) = (P x T x R) / 100

• P = (100 x C.I.) / (R x T)

• T = (100 x C.I.) / (P x R)

• R = (100 x C.I.) / (P x T)

 

So, this is basically the general idea of interest and compound interest. Now if you have any thing to know then please feel free to ask us. We will clarify your doubts here in www.AptitudeTricks.com.

Quantitative Aptitude – Time and Distance

A very important and very common topic in every competitive exams is Time and Distance. Problems on this chapter are very common in exams. So you need to learn this chapter very carefully. Also formulas of time and distance chapter will help you in further topics.

So, let’s begin the basic concept of Time and Distance.

What is Time and Distance ?

Before going further you should know that time and distance is closely related to Speed. So, what is time and distance and speed ?

Definition: The basic concept of time, distance and speed is – “A Distance covered by an object in a certain Speed for an unit of Time.”

For example, A Bus traveled 5KM at 60 km/hr in 5 minutes. So, here

• Distance = 5KM
• Speed = 60 km/hr
• Time = 5 minutes

Any object in this world when move from one place to another place it basically covered a distance. This distance can be measure in measuring unit like kilometer, meter etc. When the object moved it needs time to move from one place to another and it can be measured in hours or seconds etc. And finally the speed. When anything needs move it must have speed. So to move from one place to another an object need speed. This basically the idea about time, distance and speed.

 

Basic Formulas of Time and Distance

• Speed = Distance / Time

• Time = Distance / Speed

• Distance = Speed X Time

Unit Conversion (km/hr to m/sec)

• A km/hr = ( A X 5/18 ) m/sec

Unit Conversion (m/sec to km/hr)

• A m/sec = ( A X 18/5 ) km/hr

This is the basics of Time Distance and Speed. We hope you can now do any kind of problem using the above rules. If you want to read more about this topic then please let us know or find a good book of of Quantitative Aptitude or simply google it. We will discuss on those problems here in www.AptitudeTricks.com.

Quantitative Aptitude – Alligation or Mixture

Alligation or Mixture is an important chapter for competitive exams. Questions are often comes from this topic. Questions of this chapter are not so hard to solve. It just need a very good learning and practice of this topic.

To understand the concept of Alligation or Mixture, you need to learn the basic idea and formulas of this chapter. So, Now we will discuss the basic concept of Alligation or Mixture.

 

What is Alligation ?

Definition: Alligation helps us to find out the ratio in which two or more ingredients are mixed together to become a mixture of desired price.

So, Let’s explain this,

Suppose, we want to mix water and milk together. Price of 1 liter water is Rs.10 and price of 1 liter milk is Rs.40. Now we need to mix these two ingredients in such a ratio that we can get 1 liter of mixture at Rs.25. This is the basic concept of Alligation.

Types of Alligation

Alligation is basically of two types.

• Alligation Medial
• Alligation Alternate

 

What is Mean Price ?

Definition: Mean price is the cost of a unit quantity of the mixture.

So, we can say that the average price of a mixture is a mean price.

 

Rule of Alligation

If two ingredients are mixes, then

 

 

 

∴ (Cheaper quantity) : (Dearer quantity) = (D – M) : (M – C)

 

Finally, Suppose a container contains x of liquid from which y units are taken out and replaced by water.

• After n operations, the quantity of pure liquid = [ x{1-(y/x)}ⁿ ] units.

 

So, this is the basic idea of Alligation and Mixture chapter. Now, if you have any questions in your mind then please feel free to ask us here in www.AptitudeTricks.com. Our team member will respond to your questions later.

Quantitative Aptitude – Height and Distance

Height and distance is one of the very important topic of Quantitative Aptitude which frequently comes in competitive exams. To do a height and distance math problems you need to have a knowledge of Trigonometry. Here we will try to give you some basic idea about this topic and some formulas to do those maths. So let’s starts the discussion on height and distance.

What is Height and Distance ?

Definition: Finding measurement of any object from a certain point is called Distance and the vertical distance of an object is called Height.

Let’s explain this.

Sometimes we need to find out the height of a building, width of a sea, height of a tree etc. But these measurements are very tough to measure by any physical devices. You need trigonometric formulas to measure them with ease.

Suppose, we want to measure the height of a tree. We will not measure this by any devices. We use trigonometric formulas for this. Here comes two very important things of measuring heights, One is Angle of Elevation and other is Angle of Depression.

 

Assume that the man in the above picture is looking at the top of the tree. His eye level is “D”. Now as he look above his eye level here creates an angle (^ox). This angle is called Angle of Elevation.

Similarly, when the man looking at the bottom at the tree, there also creates an angle. But now at the opposite side (^oy). This angle is called Angle of Depression.

So, How we can find the height of a tree. The formula for this is-

Height = tan Θ X Distance between eye and tree

So, If we want to find the height of the tree we need to find out two things. One is “A” and another is “B”.

• A = tan ^ox X D
• B= tan ^oy X D

So, Height of the tree is: A + B

 

Some Important things to know:

• Sin θ = Perpendicular / Hypotenuse

• Cos θ = Base / Hypotenuse

• Tan θ = Perpendicular / Base

• Cosec θ = 1 / Sin θ

• Sec θ = 1 / Cos θ

• Cot θ = 1 / Tan θ

 

Values of T-ratios:

θ	0O	30O (π/6)	45O (π/4)	60O (π/3)	90O (π/2)
Sin θ	0	1/2	1/√2	√3/2	1
Cos θ	1	√3/2	1/√2	1/2	0
Tan θ	0	1/√3	1	√3	Not Defined

 

So, that’s all about basics of Height and Distance. Now if you have any questions on this topic then please let us know about that. We will discuss your thoughts here in www.AptitudeTricks.com. You can comment your questions and thoughts in the comment section below. We will get back to it as soon as possible.

Quantitative Aptitude – Time and Work

Time and Work questions are very common and very important in every competitive exams. You will definitely get one or two question from time and work chapter or questions related to this topic. So, you need to learn this chapter very carefully.

Let’s start the basic concept of this chapter.

What is Time and Work ?

The main concept of time and work is to find the time needed to finish a piece of work and similarly calculate the work done within a time period.

Let’s explain this,

Suppose a workman is building a house. He takes 5 days to build a wall of that house. So, according to the time and work concept he took 5 days to finish a piece of work.

Now if we want to find out that how much work is he done in 1 day, then we need to find the average his work. He works for 5 days. So,
In 5 days he do 1 work.
Therefore, in 1 day he do 1/5 work.

So, this is the basic concept of time and work. Now we will discuss few important formulas of time and work. These formulas will help you to solve all kind of problems in the examination.

 

Basic Formulas of Time and Work

Suppose a Workman can finish a piece of work in n days, then his 1 day’s work = 1/n

• Ex. A Man can finish a job in 5 days, then his 1 day’s work is 1/5.

Suppose Workman’s 1 day’s work = 1/n, then he can finish the job in n days.

• Ex. A Man do 1/7^th of work in 1 day. So he needs 7 days to finish the whole work.
  

If a workman is twice as good as another workman, then-

• Ratio of work done by Workman 1 and Workman 2 = 2 : 1.

• Ratio of times taken by Workman 1 and Workman 2 to finish a work = 1 : 2.

 

We hope you can now do any kind of problem using the above rules. If you want to read more about this topic then please let us know or find a good book of of Quantitative Aptitude or simply google it. If you have anything to ask us then please let us know that, we will discuss those questions here in www.AptitudeTricks.com.

Quantitative Aptitude – Ratio and Proportion

Ratio and Proportion is a type of fractional number, together which represent a same unit of number. In competitive exams ratio is a very important topic. Almost every competitive exams having few questions from this topic. So, students you need to learn this chapter very carefully.

Before begin this chapter you should have a clear knowledge of Fraction number. If you need to learn it then “Click here to learn Fraction number“.

Let’s start this topic.

 

What is Ratio ?

Definition: A Ratio means How much each object is used to make the whole Unit.

Let’s explain this,

Suppose we have 30 children in a Classroom. (This is the whole unit)

Now out of those 30 children their is 12 Boys and 18 Girls. (Boys and Girls are two objects)

So the Ratio of Boys and Girls in that classroom is 12 : 18. (We use : to represent ratio)

 

Scaling Ratio: We can also scale Ratio value to up or down. I the previous example we get 12 : 18 as our ratio value. But we can further scale this value down.

• 12 : 18 = (12/6) : (18/6) = 2 : 3

So, we can also write 12 : 18 as 2 : 3. Similarly we can also upscale the value and write it as 24 : 36.

 

What is Proportion ?

Definition: When we write a statement where two different ratio are equal, that is called Proportion.

Let’s explain this,

From the previous example we learned that we can scale down 12 : 18 into 2 : 3. So here ratio 2 : 3 is equal to ratio 12 : 18. Or we can say that 2 : 3 is a proportion of 12 : 18.

We write it as- 2 : 3 = 12 : 18 or
2/3 = 12/18

One more thing to keep in mind is, when two ratio is equal then the cross product of the ratio is also equal.
2/3 = 12/18
or, 2 x 18 = 12 x 3
or, 36 = 36

 

This is the basics of Ratio and Proportion. If you want to read more about ratio and proportion then find a good book of ratio and proportion or simply google it. You can ask your question here. Our member of www.AptitudeTricks.com will answer your questions.

Quantitative Aptitude – Partnership

Partnership is a very important chapter for competitive exams. Aptitude part of almost every competitive exam consist at least one question form Partnership. Also partnership is related to few other advance topics. So, you need to learn this topic very carefully. This will help you for advance topics like profit and loss, ratio, etc.

One more thing, Partnership is closely related to Ratio. So, we recommend you to please go through the Ratio chapter and learn ratio.

 

What is Partnership ?

Definition: When Two or more people jointly run a business by investing money then they are called Partners and the deal between them is called Partnership.

Let’s explain this,

Suppose A and B run a business. A invest Rs.X in the business and B invest Rs.Y in the business.

So, A and B is known as Partners.

And the deal between them is that they will share their Profit or Loss in the ratio of,

• Investment of A : Investment of B = X : Y.

This is called Partnership.

 

Basic Rules

Rule 1: When all the partners are invested money in the business for the same amount of time, then profit or loss is divided among partners in the ratio of investment.

Suppose, A and B invested Rs.X and Rs.Y for one year in their business then their share of profit or loss will be,

• A’s share of profit or loss : B’s share of profit or loss = X : Y

 

Rule 2: When all the partners are invested money in the business for the different amount of time, then profit or loss ratio is calculated as capital multiplied by length of investment.

Suppose, A and B invested Rs.X and Rs.Y for ‘m’ years and ‘n’ years in their business then their share of profit or loss will be,

A’s share of profit or loss : B’s share of profit or loss = X*m : Y*n

 

So, we hope you can now do any kind of problem using the above rule. If you need any farther help on this chapter, then please let us know. We will discuss on those problems here in www.AptitudeTricks.com.

Quantitative Aptitude – Profit and Loss

Profit and Loss is the most common and very important for the competitive exams. Questions from profit and loss will surely come in every competitive exams. And few problems from other chapter is also needed profit and loss to solve.

Now we will discuss all basics of Profit and Loss. This will brush up your knowledge of this chapter.

What is Profit and Loss ?

Before explain what is profit and loss, you need to know what is cost price and what is selling price.

Cost Price (C.P.): Cost price is the price at which an object is purchased.

Selling Price (S.P.): Selling price is the price at which an object is sold.

For example, A book shop owner purchased a book for Rs.90/- and sells the book for Rs.100/-. So, the Cost price or C.P. here is Rs.90/- and Selling price or S.P. is Rs.100/-.

 

What is Profit ?

Definition: If the selling price is greater than the cost price, the difference amount of selling price and cost price is called Profit or Gain.

So, Profit = Selling Price – Cost Price

In the above example cost price of the book was Rs.90/- and selling price of the book was Rs.100/-. S.P. is greater than the C.P. here. So, it is a profit.

Therefore,
Profit = S.P. – C.P.
Profit = 100 – 90
Profit= 10
So, the book seller earns Rs.10/- profit by selling the book.

 

What is Loss ?

Definition: If the selling price is less than the cost price, the difference amount of selling price and cost price is called Loss.

So, Loss = Cost Price – Selling Price

In the above example cost price of the book was Rs.90/- and selling price of the book was Rs.100/-. Suppose the book seller sale that book for Rs.75/-. So here S.P. is lesser than the C.P. So, it is a loss.

Therefore,
Loss = C.P. – S.P.
Loss = 90 – 75
Loss= 15
So, the book seller loss Rs.10/- by selling the book.

 

Basic Formulas of Profit and Loss

• Profit = Selling Price – Cost Price

• Loss = Cost Price – Selling Price

• Profit Percentage = (Profit x 100) / Cost Price

• Loss Percentage = (Loss x 100) / Cost Price

• Selling Price = ((100 + Profit %) / 100) x Cost Price

• Selling Price = ((100 – Loss %) / 100) x Cost Price

• Cost Price = (100 / (100 + Profit %)) x Selling Price

• Cost Price = (100 / (100 + Profit %)) x Selling Price

 

Few Examples of Profit and Loss

[mlw_quizmaster quiz=2]
 

So, we hope you can now do any kind of problem using the above rule. If you need any farther help on this chapter, then please let us know. We will discuss on those problems here in www.AptitudeTricks.com.