Ratio and Proportions : Tricks, questions and Formulae

Ratio and proportion is a very general topic for all bank exams. Mostly bank exams includes this topic in quantitative section.

Ratio is a quantity which represents the relationship between two similar quantities. It expresses a magnitude by which quantity is multiple of another one. Ratio is represented as 2:3 or 2/3. Here, numerator i.e. 2 is known as "ANTECEDENT" and denominator i.e. 3 is known as "CONSEQUENT".

If antecedent is more than the consequent, then it is known as improper ratio and if less ,then it is known as proper ratio.

Some important points:

1) If ratio is written as A:B, it is said to be a linear form and in case it is written as A/B, it is said to be fractional form.

2) Ratio does not have any unit. It is mere number.

3) The equality of two ratios is known as proportion i.e. a/b = c/d

If a/b = c/d , then it is also equal to a+c/b+d

Invertendo : If a/b = c/d , then b/a = d/c

Alterendo : If a/b = c/d , then a/c = b/d

Componendo : If a/b = c/d , then a+b/b = c+d/d

Dividendo : If a/b = c/d , then a-b/b = c-d/d

Componendo and Dividendo : If a/b = c/d , then a+b/a-b = c+d/c-d

4) If a/b = b/c = c/d =...... so on, then a,b,c,d... are in G.P.

Proof: Let a/b = b/c = c/d =k 
c= dk, b= ck, a= bk
Therefore, b= dk^2 and a= dk^2
All are in G.P.

5) If a>b and same positive number is added to each term, then ratio decreases.
For example: a/b = 4/3 = 1.3, If 2 is added to each term, then a/b = 4+2/3+2 = 6/5 = 1.2
Therefore, ratio decreases.

6) If a<b and same positive number is added to each term, then ratio increases.
For example: a/b = 3/4 = 0.7, If 2 is added to each term, then a/b = 3+2/4+2 = 5/6 = 0.8 
Therefore, ratio increases.

7) If we multiply or divide any number, there will be no effect on ratio.

8) Let a:b is a ratio

a^2:b^2 is duplicate ratio of a:b
a^3:b^3 is triplicate ratio of a:b
a^1/2:b^1/2 is sub-duplicate ratio of a:b
a^1/3:b^1/3 is sub-triplicate ratio of a:b

9) Proportions i.e. a:b = c:d
a and d are known to be extremes
b and c are known to be means.

10) In a:b :: c:d, d is fourth proportional to a,b and c.

11) If x is third proportional to a,b then it is written as a:b :: b:x.

Problem: 94 is divided into two parts in such a way that the fifth part of second are in ratio 3:4. The first part is?
Solution: Let these parts are A and B

A/5 = 3 , This implies, A = 15
B/8 4 B 32
1st part = 94*15 = Rs30
47

Read More

LCM and HCF tricks, problems and formulas

LCM i.e. least common multiple is a number which is multiple of two or more than two numbers. For example: The common multiples of 3 and 4 are 12,24 and so on. Therefore, l.c.m.is smallest positive number that is multiple of both. Here, l.c.m. is 12.. HCF i.e. highest common factor are those integral values of number that can divide that number. LCM and HCF problems are very important part of all competitive exams. 

Some important l.c.m. and h.c.f. tricks:

1) Product of two numbers = Their h.c.f. * Their l.c.m.

2) h.c.f. of given numbers always divides their l.c.m.

3) h.c.f. of given fractions =     h.c.f. of numerator     
                                                l.c.m. of denominator

4) l.c.m. of given fractions =    l.c.m. of numerator     
                                               h.c.f. of denominator

5) If d is the h.c.f. of two positive integer a and b, then there exist unique integer m and n, such that
     d = am + bn

6) If p is prime and a,b are any integer then P ,This implies   P or P
                                                                     ab                       a      b

7) h.c.f. of a given number always divides its l.c.m.

Most important points about l.c.m. and h.c.f. problems :

1) Largest number which divides x,y,z to leave same remainder = h.c.f. of y-x, z-y, z-x.

2) Largest number which divides x,y,z to leave remainder R (i.e. same) = h.c.f of x-R, y-R, z-R.

3) Largest number which divides x,y,z to leave same remainder a,b,c  = h.c.f. of x-a, y-b, z-c.

4) Least number which when divided by x,y,z and leaves a remainder R in each case = ( l.c.m. of x,y,z) + R

HCF and LCM questions:

Problem 1: Least number which when divided by 35,45,55 and leaves remainder 18,28,38; is?
Solution: i) In this case we will evaluate l.c.m.
               ii) Here the difference between every divisor and remainder is same i.e. 17.
                  Therefore, required number = l.c.m. of (35,45,55)-17 = (3465-17)= 3448.

Problem 2: Least number which when divided by 5,6,7,8 and leaves remainder 3, but when divided by 9, leaves no remainder?
Solution: l.c.m. of 5,6,7,8 = 840
                 Required number = 840 k + 3
                 Least value of k for which (840 k + 3) is divided by 9 is 2
Therefore, required number = 840*2 + 3
                                            = 1683

Problem 3: Greater number of 4 digits which is divisible by each one of 12,18,21 and 28 is?
Solution: l.c.m. of 12,18,21,28 = 254
               Therefore, required number must be divisible by 254.
               Greatest four digit number = 9999
               On dividing 9999 by 252, remainder = 171
               Therefore, 9999-171 = 9828.

Read More

3 Mistakes to avoid in IBPS and other recruitment exams

IBPS exams are one of the toughest exams due to sectional cutoffs in the exams. Many of the candidates score well in aggregate but score really low in one section which results in failure. Today I am going to give you three tips that can help you crack IBPS exams  Please read them carefully :-

Wasting lots of time on reasoning section

Reasoning is the toughest section in IBPS exams, it is tough for all so cutoffs in this section remains low. Many candidates in fear of scoring less marks, waste lots if time in this section and try to attempt question which they left in first attempt . This is a blunder and you should avoid this , 14-15 marks out of 50 are enough to clear sectional cutoff . If you are not good at this section then try to score high on other sectons . Try to score marks in every section that are required to clear cutoffs. You should follow a strategy to crack the exam.

Sticking to a question

Many times candidates stuck in a single question of quantitative section. I suggest you to skip questions which you are not able to solve within five minutes . In many case when students stuck on question sets, they waste even half hour in expectation of getting 5 questions right at once . Avoid this mistake . Get our free notes to prepare for exams.

Unable to make calculations mentally

IBPS and bank exams are very lengthy and can never be completed with mental calculations. Many candidates stuck in data interpretation questions because these questions demands lengthy calculations although they are really easy. You can increase your calculation speed by using these methods

• Learn tables from 2 to 35
• Learn square (technique) and square root of first 50 whole numbers
• Learn cube and cube root of first 30 whole numbers
• Practice to make calculations without using paper and pen
• Read quicker maths book deeply
• Learn shortcut tricks to solve questions, you can find tricks in this book.

Read More

Time management in IBPS and other jobs exams

IBPS PO and clerk is one of the easiest exams but still still students finds it very difficult to succeed. Most of the candidates finds to difficult to manage time and unable to attempt questions which can be solved in no time.

1. Attempt reasoning section at last

Reasoning is the most difficult section of IBPS and other job exams. Cutoff of this section remain low but candidates waste their time in attempting all questions of this section. Most of times examiner place this section in front of question booklet. I suggest to attempt this section at last. Try to to learn the "Question Skipping" technique, never waste your limited time in attempting difficult questions. As every question carries equal marks so try to attempt easy questions. Surprisingly 80% of the questions are very easy and can be solved in fraction of seconds.

2. Never divide time equally among all sections

Normally there are four sections in IBPS exams, but quantitative aptitude sectiontakes more time relatively. Where as English, General awareness and computer section takes relatively less time. You can devote 15 minutes more to each Quantitative and reasoning sections. It is wise to devote more time to quantitative aptitude as this is the most scoring section of exam.

3. Use shortcuts 

Try to learn shortcut techniques while solving quantitative aptitude questions. Go to Buy Books and Study notes sections to get material to learn these techniques shortcut techniques. I also started shortcut techniques series, so stay updated.

Read More

How to Score High Marks in Quantitative Aptitude Section of Bank exams

Quantitative aptitude is one of the toughest part of bank po, ibps or any other govt exam. Although most of the candidates afraid from quantitative section but it is the most scoring subject. Normally there are 50 questions in quantitative section, out of 50, 20 are easy. In most of the exams cutoffhovers around 23-24. So let's discuss some basic maths tricks to get high scores in quantitative section.

During exam preparations

1. Learn tables, squares and cubes

Learn tables up to 35 thoroughly. Similarly squares up to 50 (Squaring Technique)and cubes up to 20. It really makes calculations easy and increase your question solving ability. Most of the candidates fails due to lack of time and major part of their time is wasted on calculations in quantitative and reasoning section.

2. Learn some shortcuts

There are too many short-term tricks to solve quantitative problems. For every chapter let it time distance, number system, profit and loss or equation, there are shortcuts available. You can download some shortcut notes. I found a nice book Quicker Maths, this book has hundreds of short tricks, every institute make notes from this book. Refer to my earlier post to find this book online.

3. Refer to some comprehensive books

Many students try to score well just by solving some question from magazines and workbooks. Although these methods are good to increase your scores after you learn all the basics. But to learn basics you need to refer some good books. Read my earlier post to learn more about beat books for bank exams preparations.

4. Solve, solve and solve

The more questions you solve, higher your accuracy will be. Try to solve more questions of each chapter. Solve question of every type whichever you face.

During exam

1. Skip questions

Out of 50 questions you need to score 20+ . There are 5-6 questions of high difficulty level, it's better to skip them then wasting time on them. Finding and skipping long and difficult is a skill, you need to master this. Even in 4-5 questions set of quantitative or receiving asking section, if you are not able to understand the question or clueless about how to solve it, skip it or you will end having very low attempt.

2. Play with options

7-8 questions in an exam can be solved just by eliminating the options. Take an example,

A man bought 18 oranges for 100 rupees and sold 12 oranges for 100 rupees. Calculated profit percentage.

a) 33.333%

b) 50%

c) 66.666%

d) Can't be determined

It can be easily seen that man saved 50% of what he sold. He saved 6 oranges while he sold 12 oranges. Clearly answer is 50% 

3. Estimation

Try to estimate answer. You can 't solve 200 and more questions in 2 hours. This trick can be used in profit and loss, time distance, data interpretation and many more chapters.

4. Take 100 as base

Many questions can be solved just by taking 100 as base. Take an example

What is the percentage profit in selling an article in discount of 20% which was earlier sold for 40% profit ?

a) 20%

b) 14%

c) 28%

d) 12%


Solution : Lets take Rs.100 as cost of article. Man was selling the article for Rs140 ( 100 cost + 40 profit ) , now he is selling at a discount of 20% , now 140*20/100 = 28. New selling price = 140-28 = 112

Answer is D

Read More

Alligation - IBPS PO and clerks prep series free

This article is a part of Free IBPS PO and clerks prep series.

Alligation method is a simplified method to solve complex average problems. Alligation also helps simplify Ratio and Proportion, Simple and compound interest, Profit and loss, Time & Distance, Time Work problemsamong others. For better understanding, a few illustrations are given below. We take weighted average in the middle and average of components on the upper left and upper right hand side resulting in ratio. 

Problem
A class of consists of 60 boys and 50 girls. Average weight of boys is 60 kgs and of girls is 40 kgs. Calculate average weight of the class.

Solution

You can solve this question either by traditional weighted average method or you can simplify the calculations by using alligation.

60-x/x-50 = 2/3

X = 56

By solving this question by alligation by taking individual averages above, as in this case 60 kg and 40 kg is individual averages(don’t know what you meant by this, correct it yourself). Take smaller average on the left hand side and bigger average on the right hand side. This is just a rule of thumb to avoid mistakes and make things easier. We always take weighted average in the middle. Then by deducting individual average from weighted average and vice versa we arrive at ratios at which these components were used.

Problem 2

There’s almost always a question on mixtures in a number of competitive exams. Here's an example.

In what ratio should water be mixed with wine worth Rs. 60 per litre so that the seller earns a profit of 25% after selling the mixture for Rs. 50 per litre.

Solution 

Let's assume water is available for free,

Cost price of mixture sold is 50 *80/100= 40, as 1/4 profit on sales price = 1/5 profit on cost price.

As you can see, by just deducting weighted average cost from cost of component and vice verse, we arrive at ratio of components used.

Application of Alligation in Time and distance

Problem 3

A man travels part of his journey by bicycle at 20 Km/h and remaining distance by car at speed of 70 Km/h covering the entire journey at an average speed of 50 Km/h. What is the ratio of distance covered by bicycle and car?

Solution.

Solving this problem by alligation is a matter of just a few seconds, here’s how.

As you can see in the picture, weighted average speed is 50 km/h so we keep it in the middle. Average speed of bicycle and car is taken as in visual components. We take average speed of bicycle on the left side and average speed of car on the right side (rule of thumb). By solving this simple alligation we find that ratio of time the man takes to complete the journey by bicycle and car is 2:3. But here we need to find the ratio of distance covered, so 2*20= 40 and for car 3*70=210


Ratio comes out to be 4:21.

Update - 10-October-2013 (Question requested by Chitra Salin)

Problem 4 - This is from the practice section from PERCENTAGE notes given in website..pls help to solve either in alligation method or any

A water tank contains 5% salt by weight. x litres of fresh water is added to 40 litres of tank water, so that the solution contains 2% salt. The value of x is

a) 40 b) 50 c) 55 d) 60

Solution -
Percentage of water in current mixture = (100 - 5) = 95%
Percentage of water in output mixture = (100 - 2 ) = 98%

Ratio of mixture and fresh water is 2:3. If there was 40 litres of mixture already available in the tank, we need add 40 ×  3/2 = 60 litres

So the answer is D 

Read More

Important Geographical Facts

Indian rivers & other names:

Name of the River	Other Name
Indus	Sindhu
Brahmaputra	Dihang
Chenab	Asikini, Chandrabhagha
Jhelum	Vitasta, Hydaspes
Luni	Sagarmati
Beas	Vipasa, Hyphasis
Ravi	Parusni, Airavati
Krishna	Kanhapenna
Kosi	Kausika
Narmada	Namade
Ghaghara	Karnali

Mouths of Rivers of the world

Name of the river	Origin of the river
Nile	Mediterranean Sea
Congo	Atlantic Ocean
Amazon	Atlantic Ocean
Volga	Caspian Sea
Irrawaddy	Andaman Sea
Thames	North Sea
Mekong	South China sea
Indus	Arabian Sea
Danube	Black sea
Rhine	North sea

Names of Cyclones in different countries:

Origin of Cyclones	Name
North Atlantic (including Caribbean and Gulf of Mexico)	Hurricanes
Eastern and Central North Pacific	Hurricanes
Western Northern Pacific	Typhoons
Arabian Sea/Northern Indian Ocean	Tropical Cyclones
South Indian Ocean	Tropical Cyclones
Australia	Willy-Willy

Major Plates in the World:

Name of the plates
North American (with western Atlantic floor separated from the South American plate along the Caribbean islands) plate
South American (with western Atlantic floor separated from the North American plate along the Caribbean islands) plate
Pacific plate
India-Australia-New Zealand plate
Africa with the eastern Atlantic floor plate
Eurasia and the adjacent oceanic plate.

Minor Plates:

Name of the plate	Located in
Cocos plate	Between Central America and Pacific plate
Nazca plate	Between South America and Pacific plate
Arabian plate	Mostly the Saudi Arabian landmass
Philippine plate	Between the Asiatic and Pacific plate
Caroline plate	Between the Philippine and Indian plate (North of New Guinea)
Fuji plate	North-east of Australia

Tides:

• The rise and fall of the ocean water at a particular place are called tides. 
• Interval between two high tides or low tides is exactly 12 hours 25 minutes. Tides are produced as a result of the gravitational pull of the moon and the Sun on the earth.
• The highest tides in the world occur in the Bay of Fundy in Nova Scotia, Canada. The tidal bulge is 15 - 16 m.

Lunar day:

• Lunar day is equal to the period of one rotation of the earth on its axis with respect to the moon, or the duration of time between successive crossings of a meridian by the moon, about 24 hours 50 minutes.

Mesosphere:

• A layer of the atmosphere lying between the Stratosphere and the Ionosphere is known as Mesosphere. In the mesosphere, temperature decreases as the altitude increases. 
• The upper boundary of the mesosphere is the mesopause. 

Lithosphere:

• The rigid part of the earth’s crust that extends from a depth of about 65km (40 miles) below the surface is known as Lithosphere. It consists Sial, the Sima, and the upper Mantle. 
• Underneath it is ‘the softer, this layer known as the Asthenosphere. 

Archipelago:

• A group of islands is known as Archipelago. The name of World’s biggest Archipelago is Malay Archipelago.

Read More