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Showing posts with label quantitative aptitude. Show all posts
Showing posts with label quantitative aptitude. Show all posts

27 April 2020

Data Interpretation Shortcut Techniques - DI For UGC NET Exam with Practice Test | Quantitative Aptitude Data Interpretation

Data Interpretation Shortcut Techniques

DI For UGC NET Exam with Practice Test

SBI PO Quantitative Aptitude Data Interpretation


We are going to share with you a Quantitative Aptitude Quiz For SBI PO/Clerk Prelims, as well as for UGC NET Paper 1. First of all, we are going to share a video lecture related to the Data Interpretation basics and various DI questions with a complete solution by using shortcuts. After that, we will share DI Quantitative Aptitude Practice test.

Numerical Ability/Quantitative Aptitude Section has given butterflies to the candidates when they appear in a bank exam such as SBI PO, Clerk, and other banking examinations. The quantitative aptitude questions asked in the examination are calculative and very time-consuming. But the one who prepares for the examination with proper strategy, speed, and accuracy, this section can get you the maximum marks in any bank, ugc net and other competitive examination.

First of all you should have to watch the complete video tutorial very carefully to understand DI basics after that you will easily find the solutions of the Practice test.


Major Key points About DATA INTERPRETATION BAR GRAPHS:
1.    Don’t worry when you are connected with AAA bright academy on YouTube channel as well as with GovtJobsPortal.IN at home in this current situation especially for Various competitive exams including UGC NET, Banking, SSC, and other state-level exams.

2.    Very Vital topic  with respect to any of the following exams like SSC, UGC, banking, CDS, state government exams, railways, hotel management, law entrance, and many more exams.

3.    UGC NET STUDENTS don’t fear of data interpretation because after watching this video lecture, you will easily handle the problem of bar graphs. You will love data interpretation after watching this lecture.

4.    Easy ways and techniques to apply on questions for solving basic percentage calculations.

5.    This video tutorial is necessary for all beginners students if they want to appear in any competitive exams.

6.    DI is a process of making a sense out of the collection of data.

7.    We are going to share 2 bar graphs under the practice test section below. On the basis of those Graphs, we are sharing 10 good questions for practice.

8.    We have Two special faculties appointed for doubts daily from 11am to 6pm, to check the mobile number watch the video you will find the number on the video screen.


Watch the Data Interpretation Class

DI - BAR GRAPHS PRACTICE TEST
DIRECTION (1-5): The bar graph given below shows the percentage distribution of the total expenditures of a company under various expense heads during 2019.

13 April 2020

Ratio and Proportion Maths Class 4 : Mathematics Class for Competitive Exams

Ratio and Proportion Maths Class 4

Maths Class for Competitive Exams


Maths classes for competitive exams. We are sharing Maths classes with our readers during this curfew time because there is no notification related to the Government jobs in India. As a result, we decide to help our readers in preparing for the competitive exams during this curfew time. We are ready shared Lecture Number:1,2 and 3 related to Ratio and proportion Maths on in this Sarkari job portal.




This time we are sharing the Maths class tutorial related to the Ratio and Proportions Lecture Number 4. Along with the Maths class for competitive exams, we will share the PRACTICE TEST below. First, watch the video tutorial and then try to solve these Ratio and Proportion problems. Stay at home and practice hard for the competitive exam to have a bright future ahead after curfew. 😊.

WATCH VIDEO TUTORIAL

PRACTICE QUESTIONS OF RATIO AND PROP – 4
1.) 840 liters of a mixture contains milk and water in the ratio of 7:3. How much more water is to be added to get a new mixture containing milk and water in the ratio of 7:5.    
(Ans 168)

2.) 350 liters of a mixture contains milk and water in the ratio of 3:2. How much more water is to be added to get a new mixture containing milk and water in the ratio of 1:2.    
(Ans 280)

3.) 40 liters of a mixture containing 10% of water. How much more water is to be added to make water 20% in the new mixture.
(Ans 5)
ratio and proportion maths class

29 August 2018

Multiplication Tricks - Aptitude Tricks on How to Multiply fast

Multiplication Tricks to multiply fast. Maths tricks for Fast calculation. Multiply Trick for all the candidates who are preparing for the upcoming competitive examination. Very easy trick to multiply fast to increase your speed to solve the aptitude questions. Continue your visit with us or you can also subscribe our YOUTUBE Channel " https://www.youtube.com/user/pank1106 " for more video updates related to the aptitude tricks and reasoning tricks for competitive bank and SSC Exam. On the regular basis we share Maths tricks and Reasoning Tricks on our YouTube channel.

As we know that there are Various multiplication method to multiply fast but in this maths tricks video tutorial which we are going to share below will explain easy Multiplication tricks to multiply fast. This aptitude Trick will make you to multiply big numbers easily with in few seconds

Mathematics Trick for multiplication of big numbers in an easy manner. These Multiplication Tricks during the Bank exam will increase your speed very fast to find the solution. These Maths tricks are very valuable for all type of Bank, SSC, Railways exam.These Multiplication Tricks are very easy to understand. Just watch this Maths tricks Tutorial very carefully to understand. Those who are preparing for Bank exam this tutorial will really help you. EXPERT FACULTY MEMBER explain the things very clearly related to Multiplication tricks. In future we will share more Maths tricks and Multiplication tricks with you viewers, just subscribe our Channel for More Video Tutorials. Thanks for Watching Maths Shortcut video tutorial. Next tutorial will be on Maths tricks for fast calculation.

20 April 2017

Time, Work and Wages Problems For Bank Exam - Work and wages Concept and Shotcut

Time, Work and Wages Problems For Bank Exam

Quantitative Aptitude Study Notes for Bank Exam
Complete work and wages concept
work and wages Shortcut
You know that quantitative aptitude section is most important in bank exams in PO and Clerk and for other competitive exams because if you want good score in bank exam then you have to score good in math's. In competitive exams the most important thing is time management, if you know how to manage your time then you can do well in Bank Exams as well as in other competitive exams. That’s where maths shortcut tricks and formula are comes into action. 
Time, Work and Wages Problems For Bank Exam

So continuously we are providing shortcut tricks on different maths topics. Today’s topic is time and wages problems for bank exam. This is the one of the most important topic in quantitative aptitude section in bank and SSC exam. You should know how to solve time and wages questions in very short time for bank exam. From this chapter around 1-2 questions are given in the SBI and IBPS exams. For this here we are providing shortcut tricks and quicker method to solve time, work and wages problems in very short time. This topic is similar to the time and work problems topic but the only difference is that in this topic we will also find out wages of the workers according to their time for that particular work. Time and wages formulas: If ‘M1’ persons can do ‘W1’ work in ‘D1’ days and ‘M2’ persons can do ‘W2’ work in ‘D2’ days then we have a very special general formula in the relationship of M1 D1 W2 = M2 D2 W1.

19 April 2017

Time and Work Problems For Bank Exam

Time and Work Problems For Bank Exam

Quantitative Aptitude Study Notes for Bank Exam
Time and Work Problems For Bank Exam
You know that quantitative aptitude section is most important in bank exams in PO and Clerk and for other competitive exams because if you want good score in bank exam then you have to score good in maths. In competitive exams the most important thing is time management, if you know how to manage your time then you can do well in Bank Exams as well as in other competitive exams. That’s where maths shortcut tricks and formula are comes into action. So continuously we are providing shortcut tricks on different maths topics. Today’s topic is time and work problems for bank exam. This is the one of the most important topic in quantitative aptitude section in bank and SSC exam. You should know how to solve time and work questions in very short time for bank exam. From this chapter around 1-2 questions are given in the SBI and IBPS exams. For this here we are providing shortcut tricks and quicker method to solve time and work problems in very short time. Before going to solve questions for time and work, we study little bit about basics and formulas for time and work. If ‘M1’ persons can do ‘W1’ work in ‘D1’ days and ‘M2’ persons can do ‘W2’ work in ‘D2’ days then we have a very special general formula in the relationship of M1 D1 W2 = M2 D2 W1. The above relationship can be taken as a very basic and all-in-one formula. We also derive:

17 April 2017

Compound Interest Problems For A Bank Exam

Compound Interest Problems For A Bank Exam

 Quantitative Aptitude Study Notes for Bank Exam
Compound Interest Problems For A Bank Exam
You know that quantitative aptitude section is most important in bank exams in PO and Clerk and for other competitive exams because if you want good score in bank exam then you have to score good in maths. In competitive exams the most important thing is time management, if you know how to manage your time then you can do well in Bank Exams as well as in other competitive exams. That’s where maths shortcut tricks and formula are comes into action. So continuously we are providing shortcut tricks on different maths topics. Today’s topic is Compound Interest. This is the one of the most important topic in quantitative aptitude section in bank and SSC exam. You should know how to compound interest problems in very short time for bank exam. From this chapter around 1-2 questions are given in the SBI and IBPS exams. For this here we are providing shortcut tricks and quicker method to solve compound interest problems in very short time.  Interest is the money paid by the borrower to the lender for the use of money lent. The sum lent is called the principal. Interest is usually calculated at the rate of so many rupees for every Rs 100 of the money lent for a year. This is called the rate per cent per annul.

16 April 2017

Simple Interest Quantitative Aptitude Study Notes for Bank Exam

Simple Interest Quantitative Aptitude Study Notes for Bank Exam
Simple Interest Quantitative Aptitude Study Notes for Bank Exam
You know that quantitative aptitude section is most important in bank exams in PO and Clerk and for other competitive exams because if you want good score in bank exam then you have to score good in maths. In competitive exams the most important thing is time management, if you know how to manage your time then you can do well in Bank Exams as well as in other competitive exams. That’s where maths shortcut tricks and formula are comes into action. So continuously we are providing shortcut tricks on different maths topics. Today’s topic is Simple Interest. This is the one of the most important topic in quantitative aptitude section in bank and SSC exam. You should know how to simple interest questions and answers in very short time for bank exam. From this chapter around 1-2 questions are given in the SBI and IBPS exams. For this here we are providing shortcut tricks and quicker method to solve simple interest problems in very short time.  Interest is the money paid by the borrower to the lender for the use of money lent. The sum lent is called the principal. Interest is usually calculated at the rate of so many rupees for every Rs 100 of the money lent for a year. This is called the rate per cent per annum.

12 April 2017

PROBABILITY (Introduction and Concepts)

PROBABILITY (Introduction and Concepts)

Quantitative Aptitude Study Notes for Bank & SSC Exam
PROBABILITY (Introduction and Concepts)
You know that quantitative aptitude section is most important in bank exams in PO and Clerk and for other competitive exams because if you want good score in bank exam then you have to score good in maths. In competitive exams the most important thing is time management, if you know how to manage your time then you can do well in Bank Exams as well as in other competitive exams. That’s where maths shortcut tricks and formula are comes into action. So continuously we are providing shortcut tricks on different maths topics. Today’s topic is Probability. This is the one of the most important topic in quantitative aptitude section in bank and SSC exam. You should know how to probability questions and answers in very short time for bank exam. From this chapter around 1-2 questions are given in the SBI and IBPS exams. For this here we are providing shortcut tricks and quicker method to solve probability problems in very short time. It is similar to previous topic permutations and combinations.

08 April 2017

PERMUTATIONS AND COMBINATIONS

PERMUTATIONS AND COMBINATIONS
Quantitative Aptitude Study Notes for Bank & SSC Exam
PERMUTATIONS AND COMBINATIONS
You know that quantitative aptitude section is most important in bank exams in PO and Clerk and for other competitive exams because if you want good score in bank exam then you have to score good in maths. In competitive exams the most important thing is time management, if you know how to manage your time then you can do well in Bank Exams as well as in other competitive exams. That’s where maths shortcut tricks and formula are comes into action. So continuously we are providing shortcut tricks on different maths topics. Today’s topic is Permutations and combinations. This is the one of the most important topic in quantitative aptitude section in bank and SSC exam. You should know how to Permutations and combinations questions and answers in very short time for bank exam. From this chapter around 1-2 questions are given in the SBI and IBPS exams. For this here we are providing shortcut tricks and quicker method to solve permutations and combinations problems in very short time.

05 April 2017

BOATS AND STREAMS QUANTITATIVE APTITUDE STUDY NOTES

BOATS AND STREAMS QUANTITATIVE APTITUDE STUDY NOTES

FOR BANK AND SSC EXAM
You know that quantitative aptitude section is most important in bank exams in PO and Clerk and for other competitive exams because if you want good score in bank exam then you have to score good in maths. In competitive exams the most important thing is time management, if you know how to manage your time then you can do well in Bank Exams. That’s where maths shortcut tricks and formula are comes into action. So continuously we are providing shortcut tricks on different maths topics.
BOATS AND STREAMS QUANTITATIVE APTITUDE STUDY NOTES
Today’s topic is BOATS AND STREAMS; this is the one of the most important topics in quantitative aptitude section in Bank and SSC exam. You should know how to calculate Boats and stream questions and answers in very short time for bank exam. From this chapter around 1-2 questions are given in the SBI and IBPS exams. For this here we are providing shortcut tricks and quicker method to calculate BOATS AND STREAMS in very short time. We also providing the theorems which are elaborate short trick formula’s for stream boat.
Introduction to Boats and Streams: Normally, by speed of the boat or swimmer we mean the speed of the boat or swimmer in still water. If the boat ( or swimmer ) moves against the stream then it is called upstream and if it moves with the stream, it is called downstream.
If the speed of the boat (or the swimmer) is x and if the speed of the stream is y then, while upstream the effective speed of the boat = x – y and while downstream the effective speed of the boat = x + y.
Here are the theorems and formula’s with short tricks for boats and streams:
Theorem 1:
if x km per hour be the man’s rate in still water, and y km per hour the rate of the current.  Then
x + y = man’s rate with current
x – y = man’s rate against current.
Adding and subtracting and then dividing by 2.
x = ½ ( man’s rate with current + his rate against current)
y = ½ ( man’s rate with current – his rate against current)

hence, we have the following two facts:
(i)                A man’s rate in still water is half the sum of his rates with and against the current.
(ii)              The rate of the current is half the difference between the rates with and against the current.
Ex. 1: A man can row upstream at 10 km/hr and downstream at 16 km/hr. Find the man’s rate in still water and the rate of the current.
Solution: Rate in still water = ½ (10 + 6) = 13 km/hr
Rate of current = ½ (16 – 10) = 3 km/hr
Ex. 2: A man swims downstream 30 km and upstream 18 km, taking 3 hrs each time. What is the velocity of current?
Solution: Man’s rate downstream = 30/3 km/hr = 10 km/hr
Man’s rate upstream = 18/3 km/hr = 6 km/hr
Velocity of stream = (10 – 6) / 2
= 2 km/hr
Ex. 3: A man can row 6 km/hr in still water. It takes him twice as long to row up as to row down the river. Find the rate of the stream.
This questions we can solve by three methods, we will discuss one by one;
Solution: method 1:
Let man’s rate upstream = x km/hr
Then, man’s rate downstream = 2x km/hr
Man’s rate in still water = ½ (x + 2x) km/hr
3x/2 = 6
Or x = 4 km/hr
Thus, man’s rate upstream = 4 km/hr
Man’s rate downstream = 8 km/hr
Rate of stream = ½ (8 – 4) = 2 km/hr

Method 2:
We have,
Up rate + down rate = 2 * rate in still water
= 2 * 6 = 12 km/hr
Also, up rate: down rate = 1:2
So, dividing 12 in in the ration of 1: 2, we get
Up rate = 4 km/hr
Down rate = 8 km/hr
Rate of stream = 8 – 4 / 2
= 2 km/hr
Method 3 (shortest Method): let the rate of stream = x km/hr
Then,
 6 + x = 2 (6-x)
Or, 3x = 6
X = 6/3 = 2 km/h
Theorem 2: for boats and streams:
A man can row x km/hr in still water. If in a stream which is following at y km/hr, it takes him z hrs to row to a place and back, the distance between the two places is z(x2 – y2 ) / 2x
Proof: man’s speed up stream = (x – y) km/hr
Man’s speed downstream = (x + y ) km/hr
Let the required distance be ‘A’ km then
BOATS AND STREAMS QUANTITATIVE APTITUDE STUDY NOTES

Or, 2Ax / x2 – y2 = z
The required distance = z(x2 – y2) / 2x

Ex. 4: A man can row 6 km/hr in still water. When the river is running at 1.2 km/hr, it takes him 1 hour to row to a place and back. How far is the place?
Solution: Man’s rate downstream = (6 + 1.2) km/hr = 7.2 km/hr
Man’s rate upstream = (6 – 1.2) km/hr = 4.8 km/hr
Let the required distance be x km. Then
x/7.2 + x/4.8 = 1
or 4.8x + 7.2x = 7.2 * 4.8
x = 7.2 * 4.8 / 12
= 2.88 km.
By direct formula: required distance = 1*(62 – (1.2)2) / 2*6
36 – 1.44 / 12
3 – 0.12
=2.88 km.
Theorem 3: for boats and streams:
A man rows a certain distance downstream in x hours and returns the same distance in y hrs. If the stream follows at the rate of z km/hr then the speed of the man  in still water is given by
Z(x+y) / y-x km/hr.

Proof: let the speed of the man in still water be ‘m’ km/hr.
Then, his upstream speed = (m - z) km/hr.
And downstream speed = (m + z) km/hr/
Now, we are given that up and down journey are equal, therefore x(m + z) = y(m – z)
Or, m(y-x) = z(x+y)
M = z(x + y) / y – x km/hr
Ex. 5: Ramesh can row a certain distance downstream in 6 hours and return the same distance in 9 hours. If the stream flows at the rate of 3 km per hour, find the speed of Ramesh in still water.
Solution:
By the above formula: Ramesh’s speed in still water = 3(9+6) / 9-6 km/hr.

For quantitative aptitude study notes on other topics CLICK HERE

For Bank and SSC exam study notes CLICK HERE

03 April 2017

QUANTITATIVE APTITUDE AGE PROBLEMS

AGE PROBLEMS WITH SOLUTIONS QUANTITATIVE APTITUDE STUDY NOTES FOR BANK AND SSC EXAM

You know that quantitative aptitude section is most important in bank exams in PO and Clerk and for other competitive exams because if you want good score in bank exam then you have to score good in maths. In competitive exams the most important thing is time management, if you know how to manage your time then you can do well in Bank Exams. That’s where maths shortcut tricks and formula are comes into action. So continuously we are providing shortcut tricks on different maths topics.
AGE PROBLEMS
Today’s topic is AGE PROBLEMS. This is the one of the most important topic in quantitative aptitude section in bank and ssc exam. You should know how to calculate Age problems questions and answers in very short time for bank exam. From this chapter around 1-2 questions are given in the SBI and IBPS exams. For this here we are providing maths shortcut tricks and quicker method to calculate quantitative apptitude questions in very short time.

27 March 2017

PIPES AND CISTERNS

Quantitative Aptitude Study Notes for Bank & SSC Exam
PIPES AND CISTERNS
You know that quantitative aptitude section is most important in bank exams in PO and Clerk and for other competitive exams because if you want good score in bank exam then you have to score good in maths. In competitive exams the most important thing is time management, if you know how to manage your time then you can do well in Bank Exams. That’s where maths shortcut tricks and formula are comes into action. So continuously we are providing shortcut tricks on different maths topics.
PIPES AND CISTERNS
 Today’s topic is PIPES AND CISTERNS. This is the one of the most important topic in quantitative aptitude section in bank and ssc exam. You should know how to calculate pipe and cisterns questions and answers in very short time for bank exam. From this chapter around 1-2 questions are given in the SBI and IBPS exams. For this here we are providing shortcut tricks and quicker method to calculate pipe and cisterns in very short time.

21 March 2017

TIME DISTANCE AND TRAINS

Quantitative Aptitude Study Notes

BANK AND SSC EXAM

TIME DISTANCE AND TRAINS
You know that quantitative aptitude section is most important in bank exams in PO and Clerk and for other competitive exams because if you want good score in bank exam then you have to score good in maths. In competitive exams the most important thing is time management, if you know how to manage your time then you can do well in Bank Exams. That’s where maths shortcut tricks and formula are comes into action. So continuously we are providing shortcut tricks on different maths topics.
TIME DISTANCE AND TRAINS
Today’s topic is TIME DISTANCE AND TRAINS, it is similar to time and distance topic which we have covered in our recent topic. This is the one of the most important topic in quantitative aptitude section in bank and ssc exam. You should know how to calculate trains questions and answers in very short time for bank exam. From this chapter around 1-2 questions are given in the SBI and IBPS exams. For this here we are providing shortcut tricks and quicker method to calculate TIME DISTANCE AND TRAINS in very short time.

20 March 2017

TIME AND DISTANCE

Quantitative Aptitude Study Notes 
 Bank & SSC Exam

TIME AND DISTANCE
You know that quantitative aptitude section is most important in bank exams in PO and Clerk and for other competitive exams because if you want good score in bank exam then you have to score good in maths. In competitive exams the most important thing is time management, if you know how to manage your time then you can do well in Bank Exams. That’s where maths shortcut tricks and formula are comes into action. So continuously we are providing shortcut tricks on different maths topics.
TIME AND DISTANCE
 Today’s topic is TIME AND DISTANCE. This is the one of the most important topic in quantitative aptitude section in bank and ssc exam. You should know how to calculate time and distance questions and answers in very short time for bank exam. From this chapter around 1-2 questions are given in the SBI and IBPS exams. For this here we are providing shortcut tricks and quicker method to calculate time and distance in very short time.
If we want to solve time and distance questions or any other type of questions, then the first thing that we need that is Formulas about that topic. So here is the list of formulas that is used in time and distance quantitative topic.

17 March 2017

PROFIT AND LOSS

Quantitative Aptitude Study Notes 
 Bank & SSC Exam

PROFIT AND LOSS
You know that quantitative aptitude section is most important in bank exams in PO and Clerk and for other competitive exams because if you want good score in bank exam then you have to score good in maths. In competitive exams the most important thing is time management, if you know how to manage your time then you can do well in Bank Exams. That’s where maths shortcut tricks and formula are comes into action. So continuously we are providing shortcut tricks on different maths topics.
The one of the most important topic in maths is PROFIT AND LOSS. You should know how to calculate profit and loss in very short time. For this here we are providing shortcut tricks and quicker method to calculate profit and loss in maths.

PROFIT AND LOSS
For profit and loss we use rule of fraction is dominant. We should understand this rule very well because it is going to be used in almost all the questions.
If our required value is greater than the supplied value, we should multiply the supplied value with a fraction which is more than one. And if our required value is less than the supplied value, we should multiply the supplied value with a fraction which is less than one.
If there is a gain of x%, the calculating figures would be 100 and (100 + x).
If there is a loss of y%, the calculating figures would be 100 and (100 - y).
If the required value is more than the supplied value, our multiplying fractions should be 100 + x / 100
Or
100 / 100 – y
(both are greater than 1).
If the required value is less than the supplied value, our multiplying fractions should be
Fractions should be 100 / 100 + x
Or
100 – y / 100
(Both are less than 1).
PROFIT = SELLING PRICE (SP) – COST PRICE (CP)
LOSS = COST PRICE (CP) – SELLING PRICE (SP)
To find the gain or loss per cent %
The profit or loss is generally reckoned as so much per cent on the cost.
GAIN OR LOSS PER CENT % = loss or gain × 100 / CP

12 March 2017

CALCULATE AVERAGE SHORTCUT TRICKS

 Quantitative Aptitude Study Notes for Bank & SSC Exam

CALCULATE AVERAGE SHORTCUT TRICKS
You know that quantitative aptitude section is most important in bank exams in PO and Clerk and for other competitive exams because if you want good score in bank exam then you have to score good in maths. In competitive exams the most important thing is time management, if you know how to manage your time then you can do well in Bank Exams. That’s where maths shortcut tricks and formula are comes into action. So continuously we are providing shortcut tricks on different maths topics.
The one of the most important topic in maths is average. You should know how to calculate Average in very short time. For this here we are providing shortcut tricks to calculate average in maths.
CALCULATE AVERAGE SHORTCUT TRICKS

AVERAGE
An average, or more accurately an arithmetic mean is, in crude terms, the sum of n different data divided by n.
HOW TO CALCULATE AVERAGE:
For example, if a batsman scores 30, 50 and 25 runs in first, second and third innings respectively, then his average runs in 3 innings is equal to
30+50+25/3; =39 runs
Therefore, the two mostly used formulas in this chapter are:
Average= total of data/no. of data
And total = average × no. of data
Important Formulae Related to Calculate Average of numbers:
1. Average of first n natural number = (n+1)/2
2. Average of first n even number = (n+1)
3. Average of first n odd number = n
4. Average of consecutive number = (First number +Last number)/2
5. Average of 1 to n odd numbers = (Last odd number+1)/2
6. Average of 1 to n even numbers = (Last even number+2)/2
7. Average of squares of first n natural numbers = [(n+1) (2n+1)]/6
8. Average of the cubes of first n natural number = [n (n+1) ^2]/4
9. Average of n multiples of any number = [Number*(n+1)]/2
Examples with shortcut tricks on how to calculate Average are given below:
Ex: the average age of 30 boys of a class is equal to 14 yrs. When the age of the class teacher is included the average becomes 15 yrs. Find the age of class teacher?
Solution: total ages of 30 boys = 14 × 30 = 420yrs.
Total ages when class teacher is included = 15 × 31 = 465yrs.
So age of class teacher = 465 – 420 = 45 yrs.
Shortcut trick: age of new entrant = new average + no. of old members × Increase in average = 15 + 30 (15-14) = 45 yrs.
Ex: the average weight of 4 men is increased by 3 kg when one of them who weigh 120kg is replaced by another man. What is weight of the new man?
Solution: by shortcut trick: if the average is increased by 3 kg, then the sum of weight increases by 3 × 4 = 12 kg.
And this increase in weight is due to the extra weight included due to the inclusion of new person.
So weight of new man = 120 + 12 = 132 kg.
We can also solve this question by Direct formula: weight of new person = weight of removed person+ no. of persons × increase in average = 120 + 4 * 3= 132 kg.
Ex: the average of marks obtained by 120 candidates in a certain examination is 35. If the average marks of passed the examination?
Solution: Let the number of passed candidates be x.
Then total marks = 120 × 35 = 39x + (120-x) * 15
Or, 4200 = 39x + 1800 – 15x
Or, 24x = 2400
X = 100
So number of passed candidates = 100.
We can also solve this question by shortcut trick direct formula:
Number of passed candidates =
total candidates ( total average – failed average) / passed average-failed average
And number of failed candidates=
Total candidates (passed average – total average) / passed average – failed average
by this, we can solve number of passed candidates = 120 (35 – 15) / 39 – 15
                                                                                          = 100
Ex: A batsman in his 17th innings makes a score of 85, and thereby increases his average by 3. What is his average after 17 innings?
Solution: let the average after 16th innings be x, then 16x + 85
= 17 (x + 3) = Total score after 17th innings.
X = 85 – 51 = 34
Average after 17 innings = x + 3 = 34 + 3 = 37
Shortcut tricks or direct formula:
Average after 16 innings = 85 – 3 * 17 = 34
Average after 17 innings = 85 – 3 (17 – 1) = 37.
Ex: a cricketer has completed 10 innings and his average is 21.5 runs. How many runs must he make in his next innings so as to raise his average to 24?
Solution: total of 10 innings = 21.5 × 10 = 215
Suppose he needs a score of x in 11th innings; then average in 11 innings = 215 + x / 11 =24
Or x, = 264 – 215 = 49
Shortcut tricks or direct formula:
Required score = 11 × 24 – 21.5 × 10 = 49
Note: the above formula is based on the theory that the difference is counted due to the score in last innings.
Ex: in a class there are 20 boys whose average age is decreased by 2 months, when one boy aged 18 years is replaced by a new boy. Find the age of the new boy.
Solution: Shortcut trick:
Age of new person = age of removed person – no. of persons × decrease in average age
= 18 – 20 × 2/12
= 18 – 10/3
= 44/3
= 14 yrs 8 months.
Also read maths study notes & shortcut tricks on these topics: