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Thursday, 23 March 2017

All About Ratio And Proportion

What is Ratio?

A ratio is a relationship between two numbers by division of the same kind. The ration of a to b is written as a : b = a / b In ratio a : b , we can say that a as the first term or antecedent and b, the second term or consequent.

Example :  The ratio 4 : 9 we can represent as  4 / 9 after this 4 is a antecedent and , consequent = 9

Rule of ration :  In ratio multiplication or division of each and every term of a ratio by the same non- zero number does not affect the ratio.


Different type of ratio problem is given in Quantitative Aptitude which is a very essential topic in banking exam. Under below given some more example for your better practice.
Anything we learn in our school days was basics and that is well enough for passing our school exams. Now the time has come to learn for our competitive exams. For this we need our basics but also we have to learn something new. That’s where shortcut tricks and formula are comes into action.

What is Proportion?

The idea of proportions is that two ratio are equal.
If a : b = c : d, we write a : b : : c : d,
Ex. 3 / 15 = 1 / 5
a and d called extremes, where as b and c called mean terms.


Proportion of quantities

the four quantities a, b, c, d said proportion then we can express it
a : b = c : d
Then a : b : : c : d  <–> ( a x d ) = ( b x c )
product of means = product of extremes.

If there is given three quantities like a, b, c of same kind then then we can say it proportion of continued.
a : b = b : c the middle number b is called mean proportion. a and c are called extreme numbers.
So, b2 = ac. ( middle number )2 = ( First number x Last number ).

Quiz on ratio and proportion:-

1 If P : Q : R = 2 : 3 : 4 , Then P / Q : Q / R : R / P = ?
A. 8: 9: 24
B. 7: 9: 24
C. 4: 6: 15
D. 8: 11: 24
E. None of these

2: If 2P = 3Q = 4R, Then P : Q : R = ?
A. 2: 3: 5
B. 2: 3: 4
C. 3: 5: 6
D. 1: 2: 3
E. None of these

3: If P : Q = 2 : 3 , Q : R = 4 : 5 and R : S = 6 : 7 , then P : S = ?
A. 18: 25
B. 17: 35
C. 16: 35
D. 8: 11
E. None of these

4:Rama distributes his pencil among his four friends Rakesh, Rahul, Ranjan, and Rohit in the ratio 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5 . What is the minimum number of pencils that the person should have?
A. 66
B. 64
C. 72
D. 77
E. None of these

5: Two numbers are respectively 40% and 60% more than third number. Find the ration of two numbers ?
A. 8: 7
B. 7: 9
C. 9: 11
D. 8: 13
E. None of these

6: Rs 1210 were divided among three person P, Q, R so that P : Q = 5 : 4 and Q : R = 9 : 10. Then R gets the amount.
A. 450
B. 400
C. 500
D. 375
E. None of these

7: Share Rs.4200 among joy, sanjay and bijoy in the ration 2 : 4 : 6.Find the amount received by sanjay.
A. 1200
B. 1300
C. 1400
D. 1500
E. None of these

8 :Find the mean proportional between given two number that is 64 and 49.
A. 45
B. 52
C. 54
D. 56
E. None of these

9: What number has to be added to each term of 3 : 5 to make the ratio 5 : 6 .
A. 7
B. 6
C. 8
D. 5
E. None of these

10:Rs. 385 were divided among P , Q , R in such a way that P had Rs 20 more than Q and R had Rs 15 more than P . How much was R’s share?
A. 156
B. 145
C. 152
D. 150
E. None of these

Answers with Explanation:-
1. P : Q : R = 2 : 3 : 4 .
Let P = 2k,
Q = 3k,
R = 4k.
Then,
P / Q = 2k / 3k = 2 / 3 ,
Q / R = 3k / 4k = 3 / 4
R / P = 4k / 2k = 2 / 1.
SO, P / Q : Q / R : R / P = 2 / 3 : 3 / 4 : 2 / 1 = 8 : 9 : 24.

2. Let 2P = 3Q = 4R = k ,
Then ,
P = k / 2,
Q = k / 3 ,
R = k / 4.
SO , P : Q : R = k / 2 : k / 3 : k / 4 = 6 : 4 : 3.

3. (C)

4. Rakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 2 x 60 ) = 30.
Rahul = ( 1 / 3 x 60 ) = 20.
Ranjan = ( 1 / 4 x 60 ) = 15.
Rohit = ( 1 / 5 x 60 ) = 12.
Step 3: Total number of pencils are ( 30 x + 20 x + 15 x + 12 x) = 77 x.
For minimum number of pencils x = 1 .
The person should have atleast 77 pencils.

5.Step 1: Let the third number is A
Then first number is 140% of A = 140 x A / 100 = 7A / 5 and second number is 160% of B = 160 x B / 100 = 8B /5.
Step 2: now ratio of first and second number is 7A / 5 : 8B / 5 = 35A : 40B = 7 : 8.

6. P : Q = 5 : 4, Q : R = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9.
So, P : Q : R = 5 : 4 : 40 /9 = 45 : 36 : 40
Sum of ratio terms is = ( 45 + 36 + 40 ) =121.
R share of amount is Rs (1210 x 40 / 121) = Rs. 400.

7. Amount received by sanjay.
4 / 12 X 4200 = 1400= ( related ratio / sum of ratio ) x Total amount
So, the Amount received by sanjay is 1400.

8. The mean proportion of two numbers is
Root of 64 and 49 is √8 x √ 7 = 8 x 7 = 56.
So, the mean proportional is 56.

9.Let the number to be added x , Then
3 + x / 5 + x = 5 / 6
6 ( 3 + x ) = 5 ( 5 + x )
x = ( 25 – 18 ) = 7
So , the number to be added is 7 .

10. Let Q gets Rs x. Then We can say P gets Rs (x + 20 ) and R gets Rs ( x + 35) .
x + 20 + x + x + 35 = 385
3x = 330
x = 110 .
R’s share = Rs ( 110 + 35 ) = Rs 145 .

Number Series Rules with solved Problems.

Dear Readers, 

Since many Banking exams are in the streak and Maths section is like to be out of depth for many Aspirants. Here we are sharing Rules pertained to Number Series which is prepared and provided by one of our Ardent Readers Stallon. Number series form which at least 4- 5 questions use to come in the Banking Exams. We anticipate these would be viable to all of you.

Number Series Rules with solved Problems
Series is an important chapter from banking examination point of view. Following are some of the important rules or order on which the number series can be made :-
Pure Series
Difference Series 
Ratio Series 
Mixed Series
Geometric Series
Two Tier Arithmetic Series
Other Types

1. Pure Series
In this type of number series, the number itself obeys certain order so that the character of the series can be found out.
The number itself may be.
Perfect Square
Example :
121, 144, 169, 225 ?
Answer - 256
Perfect Cube
Example :
6859, 5832, 4913, 4096, 3375, ?
Answer - 2744

2. Difference Series
Example :
1348, 1338, 1318, 1288, 1248, ?
Answer - 1198

3. Ratio Series
Example :
336, 168, 84, 42, 21, ?
Answer - 10.5

4. Mixed Series
Example :
222, 441, 1321, 2639, 7915, ?
Answer - 15827

5. Geometric Series
Example 1. 5, 35, 245, 1715, ?
Ans. 12005
Examples 2. 43923,3993, 363, 33, ?
Ans. 3

6. Two-tier Arithmetic Series

7. Other Type
To find the odd number from the number series. In this type of series the above rules are also followed.

Some Examples ;
 2, 3, 7, 22, 89, 440, 2677, 18740
Solution : ×1+1, ×2+1, ×3+1, ×4+1, ×5+1 ........
 So, 440 is replaced by 446
5, 6, 14, 40, 89, 170, 291
Solution : +12, +32, +52, +72, +92
 So, 14 is replaced by 15.
445, 221, 109, 46, 25, 114, 4
Solution : -3÷2, -3÷2........
So,46 is replaced by 53.
12, 26, 56, 116, 244, 498, 1008
Solution : ×2+2, ×2+4 ×2+6,  ........
So, 116 is replaced by 118
8, 27, 64, 125, 217, 343
Solution : 23, 33, 43, 53,.....
So, 217 is replaced by 216

Maths Capsule Day 1

All About Number Series

What is Number Series?

Number series is a arrangement of numbers in a certain order, where some numbers are wrongly put into the series of numbers and some number is missing in that series, we need to observe and find the accurate number to the series of numbers.

In competitive exams number series are given and where you need to find missing numbers. The number series are come in different types. At first you have to decided what type of series are given in papers then according with this you have to use shortcut tricks as fast as you can .

Different types of Number Series

There are some format of series which are given in Exams.

Perfect Square Series:

This Types of Series are based on square of a number which is in same order and one square number is missing in that given series.

Example 1: 441, 484, 529, 576?

Answer: 441 = 212, 484 = 222, 529 = 232, 576 = 24, 625 = 252.

Perfect Cube Series: 

This Types of Series are based on cube of a number which is in same order and one cube number is missing in that given series

Example 2: 1331, 1728, 2197, ?

Answer : 113 ,  123 ,  133 ,  143 

Geometric Series:

This type of series are based on ascending or descending order of numbers and each successive number is obtain by multiplying or dividing the previous number with a fixed number.

Example 3: 5, 45, 405, 3645,?

Answer: 5 x 9 = 45, 45 x 9 = 405, 405 x 9 = 3645, 3645 x 9 = 32805.

Two stage Type Series:

A two tier Arithmetic series is one in which the differences of successive numbers themselves form an arithmetic series.

Example 4: i. 3, 9, 18, 35, 58,——

ii. 6, 9, 17, 23,———-


Mixed Series:

This type of series are more than one different order are given in a series which arranged in alternatively in a single series or created according to any non-conventional rule. This mixed series Examples are describes in separately.

Examples 5: 

11, 24, 50, 102, 206, ?

Answer: 

11 x 2 = 22 +2 = 24,

24 x 2 = 48 + 2 = 50,

50 x 2 = 100 + 2 = 102,

102 x 2 = 204 + 2 = 206,

206 x 2 = 412 + 2 = 414.
So the missing number is 414.

Number Series Quiz

Directions (1-10): What will come in place of the question marks (?) in the following Number series?
1.    0, 6, 24, 60, 120, 210, ?
A.  336       
B.  349
C.  312
D.  337
E.  None of these

2.    11, 14, 19, 22, 27, 30, ?
A.  39
B.  34
C.  36
D.  35
E.  None of these

3.    6, 12, 21, ? , 48
A.  33
B.  39
C.  36
D.  31
E.  None of these

4.    18, 22, 30, ? ,78, 142
A.  44
B.  35
C.  46
D.  48
E.  None of these

5.    73205, 6655, 605, 55, ?
A.  9
B.  5
C.  13
D.  11
E.  None of these

6.    25, 100, ?, 1600, 6400
A.  400
B.  300
C.  360
D.  420
E.  None of these

7.    125, ?, 343, 512, 729, 1000
A.  216
B.  215
C.  256
D.  225
E.  None of these

8.    1 , 9 , 125 , 343 , ? , 1331
A.  730
B.  729
C.  512
D.  772
E.  None of these

9.    121, 144, 169, ?, 225
A.  180
B.  172
C.  186
D.  196
E.  None of these

10.  ?, 2116, 2209, 2304, 2401, 2500
A.  2124
B.  1972
C.  1521
D.  2025
E.  None of these

Answers with Explanation:-

1.     (A)
The given series is : 13 – 1, 23 – 2, 33 – 3, 43 – 4, 53 – 5, 63 – 6,
So the missing term = 73 – 7 = 343 – 7 = 336 .

2.    (D)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 30 + 5 = 35 .

3.    (A)
The pattern is + 6, + 9, + 12, +15 ………..
So the missing term is = 21 + 12 = 33 .

4.    (C)
The pattern is +4, +8, +16, +32, +64
So the missing term is = 30 + 16 = 46 .

5.    (B)
5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205

6.    (A)
25 x 4 = 100, 100 x 4 = 400, 400 x 4 = 1600, 1600 x 4 = 6400.

7.    (A)
 125 = 53 , 216 = 63, 343 = 73, 512 = 83, 729 = 93, 1000 = 103.

8.    (B)
 13 , 33 , 53 , 73 , 93 , 113

9.    (D)
121 = 112, 144 = 122, 169 = 132, 196 = 142, 225 = 152.

10.  (D)
 2025 = 452, 2116 = 462, 2304 = 482, 2401 = 492, 2500 = 502

TIME TAKEN

Within 5 min         : EXCELLENT
5-8 min                 : YOU CAN DO BETTER
More than 8 min   : YOU NEED TO WORK HARD

Wednesday, 22 March 2017

Daily English Vocab Capsule Day 7

A brief history of the past 70 years
One of the outcomes of the recently concluded Assembly elections is that India is set to have the same party ruling at the Centre and in many of the States. While this may have had some advantages in the past, such as for the decisive ending of stagnation after a century of colonial rule, a dispersion of power is desirable for our democracy. India after all is not some small European country. Not only is it set to become the world’s largest country in a matter of decades but it is also an economy challenged by poverty. There is also great cultural and religious diversity here. A governance equal to this configuration is vital.
At an ominous juncture
Therefore, the Bharatiya Janata Party’s choice of a mahant as Chief Minister of Uttar Pradesh is ominous (threateningly inauspicious) from this point of view. The politics that it represents needs to be challenged, but the question is how this is to be achieved. In the Westminster model of government that we follow, dispersion of power requires a strong opposition at the Centre. It is the absence of any real opposition to the Congress for three decades after 1947 that is responsible for India’s slow progress despite its quite spectacular beginning under Jawaharlal Nehru. Political parties become complacent (showing smug or uncritical satisfaction with oneself or one's achievements.) when they face no opposition. It has been pointed out that it is States which witnessed political competition that have made the most progress. The examples usually cited are Himachal Pradesh, Kerala and Tamil Nadu.
Thus with the BJP in power open-endedly, we may find a faster pace of development, but may find ourselves under a more authoritarian governance. It is also conceivable that despite economic buoyancy the minorities may feel alienated (पृथक करना) by the politics of Hindutva even though some of the associated rhetoric has been toned down of late. To avert both these possibilities it is important that the BJP remains challenged by a strong opposition at the Centre.
Right now this can be imagined as coming from the Congress alone for it is the only other national party though in reduced circumstances. But this cannot be guaranteed. To effectively be the opposition, India’s grand old party would have to not just rethink its strategy but reflect seriously on what it stands for today. Why have the people of U.P. chosen to vote into government a party that has not a great deal to show in terms of countrywide economic indicators? The economy has slowed and is nowhere near achieving the double-digit growth promised during the general election of 2014. Inflation is lower but far from tamed, with the price of dal, the poor man’s protein, reaching close to Rs. 200 per kg on occasion. To top it all, there was the demonetisation, which by all grassroots accounts led to a dip in output.
Yet the BJP has walked away with the prize of power in India’s largest State by far. Accounts such as that the BJP has merely “tapped into its vote bank” imply an irreversible slide, which is hopelessly pessimistic. They fail to acknowledge that the BJP has been voted out in U.P. in the past, most significantly at the first opportunity after the demolition of the Babri Masjid. It has returned to power only after a spell in the wilderness (in the wilderness means they (related figure) no longer have a position of authority), after the Bahujan Samaj Party and the Samajwadi Party had been given a chance to deliver broad-based development.
The midnight reminder
While the Congress’s leadership has said little publicly on its defeat in U.P., some of its spokespersons exhibited a thoughtfulness on television soon after when they spoke of a need to reflect deeply on the inability of the party to come up with a winning formula, so to speak. If the party ever gets down to such an exercise seriously, it need do nothing more than study Nehru’s conduct as Prime Minister. And they could make no better a start than to listen to his public address at midnight on August 14, 1947. There, between the weary (उबाऊ/थकाऊ) voice and measured cadence (a modulation or inflection of the voice.), members of today’s Congress party would find a purpose worth reclaiming. Nehru had spoken of independence as essentially an opportunity for “end (ing of) poverty and ignorance and disease and inequality of opportunity.” There is clarity in this, for Nehru could see that without it Independence would amount to no more that replacing a colonial autocracy (a system of government by one person with absolute power.) with a native one.
It is interesting that while even “prosperity” makes an appearance later in the speech ‘secularism’ is altogether missing from it. Does this mean that Nehru was somehow lacking in commitment to it? Not even his most ardent (उत्साही) critics would dare propose this. Or can it be said that Nehru could afford to not foreground secularism in a way that the Congress must today as the climate has changed considerably since? Hardly. Nehru was speaking even as communal violence enacted a deathly dance around him. And his subsequent actions speak not only for where he stood vis-a-vis (in relation to; with regard to.) the question of the role of religion in the nascent (नवजात) republic but also of the role of the government in ensuring the safety of India’s Muslims post Partition. Eyewitness accounts speak of him as a man possessed haranguing (भाषण देना) roving (घुमंतू) gangs of Hindus seeking revenge on Delhi’s streets in August 1947.
Some years later he was to ensure the re-codification of Hindu personal law with a view to redressing (सुधारना) the balance against women. Petitions seeking justice in marriage that have reached the Supreme Court from Christian and Muslim women suggest that he erred (ग़लती होना/विचलित होना)in not giving the same treatment to all religions. But he had stopped with this. Unlike the Congress after Indira Gandhi, he did not allow his commitment to safeguarding the rights of India’s minorities to be exchanged for any empowerment of the clergy (the body of all people ordained for religious duties). This was to come much later and was to take a particularly jarring form in some States where, from the women’s rights to freedom of expression for artists, the Congress has shown itself anxious to appease clergymen from the minorities.
Nothing, however, can match the cynical (Skeptical) calculations of Rajiv Gandhi, in response to the Shah Bano case and the Ram temple agitation, which appeased the most reactionary sections of Muslims and Hindus, respectively. With it the path was cleared for the rise of the BJP. It is entirely in the hands of the Congress to return to being a party that keeps religion out of politics except of course to ensure that an individual’s right to worship, without trampling (रौंद देना/कूचलना) on the rights of others, is preserved. The ideal is summed up perfectly by Nehru who had ended his speech with: “All of us, to whatever religion we may belong, are equally the children of India with equal rights, privileges and obligations.”
The Congress’s second moment after the national movement was to come in 1991 when it averted (prevent or ward off (an undesirable occurrence).) a default on India’s international obligations. Led by P.V. Narasimha Rao, it steered the country away from a diminution (अवनति/ह्रास)of its political stature that was assured were it to renege on them. There was also some contingent (निर्भर) restructuring of the economy. One need only glance at post-Communist Russia to see how the Rao-Manmohan Singh duo managed the transition with some finesse. It is only later, under the UPA, that the Congress got identified with not only dynastic privilege but also allowing economic inequality to spin out of control. Now the concerns of the corporate sector, including a hankering (लालायित होना) for recognition by the U.S., came to be privileged over that of the ordinary Indian. The government came to be seen as distant, and instances of the ingenious (cleverly and originally devised and well suited to its purpose.) use of the state apparatus to amass private wealth under a liberalised policy regime came to light. Examples of the latter range from telecom to aviation.
There’s still time
With this the path already cleared for the BJP was widened. By the time of the elections in U.P. Narendra Modi had repositioned himself as the deliverer of broad-based development, a role that historically belonged to the Congress. It was this very role that Nehru had in mind when on the eve of Independence he spoke of prosperity being “indivisible”. It is still not too late for the Congress leadership to internalise this. Above all, in the coarser language of today, Nehru had “walked the talk”. Economic inequality declined as a result of his policies and the man himself died owning far less than he had inherited.
Courtesy: The Hindu (Political)

1. Complacent (adjective): Showing smug or uncritical satisfaction with oneself or one's achievements. (संतुष्ट)
Synonyms: Smug, Self-satisfied, Self-contended.
Antonyms: Discontented, Dissatisfied.
Example: Although Chuck wanted an 'A' in the class, he was complacent with a 'B'.
Related words:
Complacency (noun) – सन्तोष
Origin: From Latin complacens, present participle of complacere to please greatly.

2. Alienate (Verb): Make (someone) feel isolated or estranged. (पृथक करना)
Synonyms: Estrange, Turn Away, Set Apart, Isolate, Detach.
Antonyms: Combine, Join, Unite.
Example: The restaurant owner hesitates to change his menu because he does not want to alienate his regular customers.
Verb forms: Alienate, Alienated, Alienated.
Origin: From Latin alienus means not one's own.

3. Weary (adjective): Feeling or showing extreme tiredness/ tiring and tedious. (उबाऊ/थकाऊ)
Synonyms: Bored, Exhausted, Tiring, Prostrate.
Antonyms: Energetic, Fresh, Invigorated.
Example: Although the police officers are weary, they will not rest until they find the missing baby.
Origin: From German werig means intoxicated.

4. Harangue (Verb): Lecture (someone) at length in an aggressive and critical manner. (भाषण देना)
Synonyms: Lecture, Rant, Tirade, Diatribe.
Example: The comedian harangued hilariously about obnoxious celebrities.
Verb forms: Harangue, Harangued, Harangued.
Related words:
Harangue (noun) - भाषण
Origin: In Old Italian, the noun "aringo" referred to a public assembly, the verb aringare meant "to speak in public," and the noun "aringa" referred to a public speech. "Aringa" was borrowed into Middle French as arenge, and it is from this form that we get our noun "harangue,".

5. Redress (Verb): Remedy or set right (an undesirable or unfair situation). (सुधारना)
Synonyms: Rectify, Correct, Right, Reform, Amend.
Antonyms: Damage.
Example: The Company hopes to redress the victim’s injury by paying out a million dollar settlement.
Verb forms: Redress, Redressed, Redressed.
Related words:
Redress (noun) - remedy or compensation for a wrong or grievance.

6. Err (Verb): Be mistaken or incorrect (ग़लती होना/विचलित होना)
Synonyms: Mistake, Blunder, Miscalculate.
Antonyms: Correct.
Example: The pharmacist carefully fills prescriptions so she will not err and harm a patient.
Verb forms: Err, Erred, Erred.
Related words:
Error (noun) - ग़लती
Origin:  From Lain Errare means to stray.

7. Trample (Verb): Tread on and crush./  to treat other people's rights, wishes, or feelings as if they are worthless or not important. (रौंद देना/कूचलना)
Synonyms: Crush, Infringe, Override.
Antonyms: Aid, Assist, Cure.
Example: In Dictatorship, rights of common people get trampled.
Verb forms: Trample, Trampled, Trampled.

8. Diminution (noun): The act, process, or an instance of becoming gradually less (as in size or importance). (अवनति/ह्रास)
Synonyms: Curtailment, Decline, Reduction.
Antonyms: Growth, Improvement, Increase.
Example: The diminution of military troops will leave our country more vulnerable to invasion.
Verb forms: Diminish, Diminished, Diminished.
Origin:  via Old French from Latin verb deminuere means to Diminish.

9. Contingent (adjective): Occurring or existing only if (certain circumstances) are the case; dependent on.  (निर्भर)
Synonyms: Dependent, Conditional, Subject To, Based On, Determined By, Hinging On.
Antonyms: Unconditional, Independent.
Example: The use of the discount coupon is contingent upon a customer purchasing at least fifty dollars worth of groceries.
Origin: from Latin contingens, present participle of contingere (com- + tangere) to have contact with, befall.

10. Hanker (Verb): To have a strong or persistent desire. (लालायित होना)
Synonym:  Crave, Want, Desire, Yearn.
Antonyms: Dislike, Hate, Despise, Be averse
Example: Since Kelly has a hankering to listen to music, she’s going to a jazz club tonight.
Verb forms: Hanker, Hankered, Hankered.
Related words:
Hankering (noun) - तीव्र इच्छा
Origin: From Dutch Hunkeren means to yearn.

Daily English Capsule Day 22

Hi, Friends, iam back with some of new actions. so please read always my blog. Hunting for Solutions In July 2015, when Cecil, a...