Maths Capsule : Multiplication

Quant Short Tricks on Multiplication

Hello Readers,

Here are some short tricks on Multiplication which might help you in Quant Section of every competitive exam. Hope you all like the post!

1. Multiplication using multiples

Assume that we should find out the result of 12 x 15. 

12 x 15   (Here we can write this 15 as 5 x 3)

=  12 x 5 x 3 (now 12 x 5 becomes 60)

=  60 x 3 (For this you just calculate 3 x 6, that is 18 and add one Zero to it. that is 180)

=  180

2. Multiplication by distribution 

Assume that we should find out the result of 12 x 17

12 x 17  

(Here we can divide this 17 as 10+7. Here, multiplying 12 with 17 is same as multiplying 12 with 10 and 7 separately and then adding the results)

so, we can write it as

= (12 x 10) + (12 x 7) 

= 120 + 84

= 204 

3. Multiplication by "giving and taking"

12 x 47  (Here its little difficult for us to calculate the multiplication of 12 and 47 mentally. so just check for the ROUNDED number nearer to 47. Yes it is 50. so.....

= 12 x (50 - 3) 

= (12 x 50) - (12 x 3)   = 600 - 36

= 564

4. Multiplication by 5

If we have to multiply a number with 5, just divide the number with 2 and then multiply the result with 10. Confused? Its very simple step actually....

428 x 5   (Now just divide the number with 2)

= 428 x 1/2 = 214 (Now multiply it with 10)

= 214 x 10

= 2140 (This is our result)

What’s the logic behind this step? 

Very simple. 

Lets say the number is X.

Now we are dividing the number with 2.  so here X becomes X/2. 

And then we are multiplying it with 10.  So it will become 10X / 2  

Now cancel it with 2. so it becomes 10X / 2 = 5X = 5 multiplied by X. That’s it ;)

5. Multiplication by 10  ------------  just move the decimal point one place to the right

16 x 10

= 160

5.9 = 159

169.93 = 169.3  

6. Multiplication by 50 ------ divide with 2 and then multiply by 100

Well, this is also same process as we did for 5. Here we should add an extra zero. That’s it

18 x 50

= (18/2)  = 9

= 9 x 100

= 900

7. Multiplication by 100 -------- move the decimal point two places to the right

45 x 100

= 4500  

8. Multiplication by 500-------- divide with two and multiply with 1000 

21 x 500

= 21/2 x 1000

= 10.5 x 1000

= 10500

9.  Multiplication by 25 ---------- use the analogy Rs 1 = 4 x 25 Paise

25 x 14 (just divide the 14 as 10+4)

= (25 x 10) + (25 x 4) 

= 250 + 100 --->  Rs2.50 + Rs1

= 350

10. Here you can use another technique too. Which we have used for multiplication with 5.

Multiplication by 25 -----------  Divide by 4 and multiply by 100 

36 x 25

= (36/4) x 100

= 9 x 100

= 900  

11. Multiplication by 11 (if sum of digits is less than 10)

72 x 11

= 7+2 =9, it is Less than 10. so,

= place this term 9 between 7 &2

= 792 (That's the answer)

12. Multiplication by 11 (if sum of digits is greater than 10)

87 x 11

=>  8 + 7 = 15 

because here 15 is greater than 10, first use 5 and then add 1 to the first term 8, 

which gives you the answer

= 957 

13. Multiplication of numbers ending in 5 with the same first terms (square of a number)

25 x 25 

first term = (2 + 1) x 2 = 6

last term = 25

answer = 625 => square of 25

75 x 75 

first term = (7 + 1) x 7 = 56

last term = 25

answer = 5625 => 75 square

Maths Capsule : Percentage

Study Notes on Percentage with Quiz

Hello Readers,

We shall discuss about Percentage of the Quant section.  Now a days these topics  have became an important part of the Quant test in not only SSC but also almost in all Entrance Exams like FCI Exams and IBPS Exam.So Here we will help you in this.We will  provide short tricks on Percentage with Quant Quiz.

Percentage: A fraction whose denominator is 100 is called percentage. and The numerator of the fraction is called the rate percent.

1. To express x% as a fraction:

We have, x% = x/100

      Thus, 30% = 30/100 =3/10

2. To express fraction as percentage,

we have ,

 a/b =  {a/b x100}%

                           

3. If A is R% more than B, then B is less than A by

  {(R/(100+R)x100}% 

4. If A is R% less than B, then B is more than A by

   {(R/(100-R)x100}% 

5. If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:

  {(R/(100+R)x100}% 

6. If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:

  {(R/(100-R)x100}% 

7. Let the population of a town be P now and suppose it increases at the rate of R% per annum, then

   1. Population after n years = P(1+R/100)^n

   2.Population before n years =P/(1 + R/100)^n

8. Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum.

   1.Value of the machine after n years= P(1-R/100)^n

                                                       
   2.Value of the machine n years ago=P/(1-R/100)^n 

                         

9. For two successive changes of x% and y%, net change

   {x + y +xy/100}%

1. A shopkeeper announces successive discounts of 10% and 20%. Find the equivalent percent discount.

A.  27%

B.  28%

C.  29%

D.  30%

2. In a college, 40% of the students were allotted group A, 75% of the remaining were given group B and the remaining 12 students were given group C. Then the number of students who applied for the groups is:

A.  80

B.  92

C.  100

D.  60

3.Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:

A. 39, 30

B. 41, 32

C. 42, 33

D.43, 34

4. In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?

A. 8200

B. 7500

C. 7000

D. 8000

5. The price of a car is Rs. 3,25,000. It was insured to 85% of its price. The car was damaged completely in an accident and the insurance company paid 90% of the insurance. What was the difference between the price of the car and the amount received ?

A. Rs. 76,375

B. Rs. 34,000

C. Rs. 82,150

D. Rs. 70,000

6. Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?

A. Rs. 15

B. Rs. 15.70

C. Rs. 19.70

D. Rs. 20

7. In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is  of the number of students of 8 years of age which is 48. What is the total number of students in the school?

A. 72

B. 80

C. 120

D. 100

8. A's salary is 30% higher than B's salary. The percent that B's salary is less than A's salary is:

A.  25%

B.  30%

C.  23 1/13%

D.  20%

9. If the price of sugar is increased by 25%, by how much percent must a householder reduce his consumption of sugar so as not to increase his expenditure on sugar?

A.  35%

B.  30%

C.  25%

D.  20%

10. In a class of 40 students and 8 teachers, each student got sweets that are 20% of the total number of students and each teacher got sweets that are 25% of the total number of students. How many sweets were there?

A.  420

B.  400

C.  320

D.  360

Answer and Solution :
1(B)Explanation
For two successive changes of x% and y%, net change =
     {x + y +xy/100}%
  = {-10-20+(-10)(-20)/100}%
  =(-30 + 2) %
  = - 28%

2(A)Explanation
Let the number of students be 100.
Number of students allotted to group A = 40
Number of students allotted to group B = 75% of 60 = 45
Thus, Balance number of students allotted to group C = 100 - 40 - 45 = 5
Number of actual students = 100/15 * 12 = 80

 3(C)Explanation:
Let their marks be (x + 9) and x.
Then, x + 9 = 56/100(x + 9 + x)
 =>25(x + 9) = 14(2x + 9)
 =>3x = 99
 =>x =33
 So, their marks are 42 and 33.

4(D)Explanation :
State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 80 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 80
=> total appeared candidates in State B = 80 x 100 = 8000
=> total appeared candidates in State A = total appeared candidates in State B = 8000

5(A)Explanation :
Price of the car = Rs.3,25,000
Car insured to 85% of its price
=>Insured price=325000×85/100
Insurance company paid 90% of the insurance
Amount paid by Insurance company =Insured price×90/100
=325000×85/100×90/100=325×85×9=Rs.248625
Difference between the price of the car and the amount received
= Rs.325000 - Rs.248625 = Rs.76375

6(C)Explanation:
Let the amount taxable purchases be Rs. x.
Then, 6% of x = 30/100
=> x = (30/100 x 100/6) = 5
so  Cost of tax free items = Rs. [25 - (5 + 0.30)] = Rs. 19.70

7(D)Explanation:
Let the number of students be x. Then,
Number of students above 8 years of age = (100 - 20)% of x = 80% of x.
so  80% of x = 48 + 2/3 of 48
=> 80/100 x = 80
=> x = 100.

8(C)Explanation:
Let B's salary be Rs. 100
Then , A's salary = Rs.130
Required percentage = 30/100 * 100 = 23 1/13%

9(D) Explanation:
If the price of a commdity increases by R% , then the reduction in consumption so as not to increase the expenditure is :
   {(R/(100+R)x100}%
Thus, percent reduction in consumption =  {(25/(100+25)x100}%
 = 20 %

 10(B)Explanation :
Number of students in the class = 40
Sweets received by 40 students = 40 * (20% of 40) = 320
Number of teachers in the class = 8
Sweets received by 8 teacher  = 8 * (25% of 40) = 80
Total number of sweets = 320 + 80 = 400

Maths Capsule : Important Short Tips of Square Root ,Cube Root and Quant Quiz

Important Short Tips of Square Root ,Cube Root and Quant Quiz

Hello Readers,
We shall discuss about Square  Root and Cube Root of the Quant section.  Now a days these topics  have became an important part of the Quant test in  SSC and also help almost all Entrance Exams like FCI Exams and IBPS Exam.So Here we will help you in this.We will  provide short Tips and quant quiz.

5. The least perfect square, which is divisible by each of 21, 36 and 66 is:

A. 213444

B. 214344

C. 214434      

D. 231444

6. How many two-digit numbers satisfy this property : The last digit (units digit) of the square of the two-digit number is 8 ?

A. 1

B. 2

C. 3

D. None of these

7.A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:

A. 57  

B. 67

C. 77  

D. 87

8. A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 98.01, the number of the member is the group is:

A. 101

B. 98

C. 99

D. 88

9.A man plants 49284 apple trees in his garden and arranges them so that there are as many rows as there are apples trees in each row. The number of rows is

A. 182

B. 202

C. 222

D. 122

10.If 0.13÷p^2=13, then p equals :

A. 0.01

B. 0.1

C. 10

D  100

ANSWER AND SOLUTION :

6(D)Explanation :

A number ending with 8 can never become a perfect square

Let's examine this in detail

1 × 1 = 1

Hence, if the unit digit of a number is 1, unit digit of its square is 1

2 × 2 = 4

Hence, if the unit digit of a number is 2, unit digit of its square is 4

3 × 3 = 9

Hence, if the unit digit of a number is 3, unit digit of its square is 9

4 × 4 = 16

Hence, if the unit digit of a number is 4, unit digit of its square is 6

5 × 5 = 25

Hence, if the unit digit of a number is 5, unit digit of its square is 5

6 × 6 = 36

Hence, if the unit digit of a number is 6, unit digit of its square is 6

7 × 7 = 49

Hence, if the unit digit of a number is 7, unit digit of its square is 9

8 × 8 = 64

Hence, if the unit digit of a number is 8, unit digit of its square is 4

9 × 9 = 81

Hence, if the unit digit of a number is 9, unit digit of its square is 1

0 × 0 = 0

Hence, if the unit digit of a number is 0, unit digit of its square is 0

Daily English Vocabulary Capsule Day 11

One India, two time zones

In a two paragraph order delivered by Chief Justice Ajit Singh, the Gauhati High Court has dismissed a public interest litigation filed by Rita Mozumder seeking a direction from the Central government to notify a separate time zone for the Northeast. The court cites a high-level committee study, constituted by the Ministry of Science and Technology, that recognised the difficulties faced by a single time zone in eastern India but concluded that Indian Standard Time (IST) should nonetheless be retained. The issues raised by the petition demanded more than a cursory (त्वरित/सरसरी) order dismissing the petition given the importance of the issue. Legislators, activists, industrialists and ordinary citizens from the Northeast have often complained about the effect of IST on their lives, and pursued the issue of having a separate time zone with the Central government, without much success. The petition arose after repeated rejections by the government.

The idea of a standard time zone has become so integral to our lives that we often take it for granted and assume it to be a part of natural phenomena. We tend to forget the complex contestations (प्रतिवाद/विवाद) — including legal ones — that go into its making. The creation of a time zone signals the victory of time over space with geographical areas being brought under a single time zone rather than relying on local solar time. It entails a denial of local time — or a separation of time from space — a very significant fact if you consider what it means to the experience of social and economic lives. In the case of India, the time difference between the westernmost part of India and the easternmost point is approximately two hours, the effect of which is that the sun rises and sets much earlier than it does in the rest of the country.

There is a strong case

In the Northeast, the sun rises as early as four in the morning and in winter it sets by four in the evening. By the time government offices or educational institutions open, many daylight hours are already lost. In winter this problem gets even more accentuated (जोर देना) and the ecological costs are a disaster with much more electricity having to be consumed. Profs. D.P. Sengupta, and Dilip Ahuja of the National Institute of Advanced Studies claim that advancing IST by half an hour would result in saving 2.7 billion units of electricity every year. None of the other proposals such as the introduction of daylight saving time in India has met with any approval and it is felt that having two time zones would be unsuitable. There is of course a strong political dimension to granting a separate time zone in the Northeast given the region’s long history of self-determination movements. The unstated assumption is that the grant of a different time zone is only the first temporal step towards conceding (स्वीकृति देना) spatial (स्थान-संबंधी) autonomy. This appears to me to be a short-sighted perspective. If socioeconomic development is indeed one of the formulae to combatinsurgency (विद्रोह), might it not be worthwhile to consider the disastrous impact that IST has on productivity and efficiency in the region?

A few years ago, then Assam Chief Minister Tarun Gogoi, frustrated with the decision of the Centre not to have a separate Northeast time,unilaterally (एकतरफ़ा) decided that Assam would follow ChaiBagaan time. Bagaan time or tea time is a reference to an informal practice followed in tea gardens in Assam which is an hour ahead of IST. It alerts us to the fact that there is indeed a long history of the application of different time zones in India. We find evidence of this in the Constituent Assembly debates. On December 28, 1948, responding to an amendment proposed by Naziruddin Ahmad, Dr. Ambedkar asked him what system of timing he had in mind: “Is it the Greenwich time, the Standard time, Bombay time or Calcutta time?”

Ambedkar’s reference to “Bombay time” and “Calcutta time” reminds us of an interesting aberration (पथांतरण /असामान्यता) in the history of IST. It was instituted in 1905 but after it had been adopted, Bombay traders found it difficult to convert to IST. Because the conversion to IST was sought to be effected at a time when there was considerable public resentment over the Tilak sedition (राजद्रोह/विद्रोह) trial, the government found little support for this shift among the people in Bombay. Bombay Time was maintained right up to 1955 with Bombay following its own time zone which was 38 minutes ahead of the rest of the country.

Our use of time

While the court may have been reticent (मितभाषी/वाक्संयमी) to intervene in what it saw primarily as an executive prerogative (विशेष अधिकर), it also passed an opportunity to examine a fascinating (आकर्षक) dimension of temporal justice that Indian courts have not had an opportunity to address, but other jurisdictions have had to contend with (Phrasal verb – to fight). In the U.S., battles over daylight-saving time regularly went to court and it was not until 1966 with the passing of the Uniform Time Act that they had a uniform national period of daylight-saving time. Todd D. Rakoff in his work on the invisibility of time in structuring the law argues that there is a normative dimension of time that seems to underwrite a number of legal arrangements, and the question of how we, as a society, structure our time is mirrored in the question how we structure our laws.

Responding to the various objections raised about a separate time zone, journalist, writer and academic Sanjoy Hazarika raises critical questions and asks us to consider why it is that the development index leans considerably in favour of western India as opposed to the east, and what impact differential time may have on it. This I believe is a question that has a significant impact on the interpretation of ‘life’ in Article 21 of the Constitution. Even if the Gauhati High Court were unwilling to issue a substantive order, it certainly had the discretion (समझ/बुद्धिमानी) to ask for a study on the legal impact of a single time zone on the fundamental rights of people. This is perhaps a question that the Law Commission may find worthy of investigating further. In the meantime, we will have to be content with the tweaking (सुधारना) of local orders changing office timings etc. And, most of east India will continue to feel the vagaries (अनिश्चितताएं) of IST an inconvenience while the further you go to the Northeast, it will be experienced as the caprice (सनक) of the state.

Courtesy: The Hindu (National).

1. Contestation (noun): The action or process of disputing or arguing. (प्रतिवाद/विवाद)

Synonyms: Disagreement, Controversy, Disputation, Dissention.

Antonyms: Accord, Agreement, Consensus, Harmony, Unanimity.

Example: Ideological contestations in India are common nowadays.

Verb forms: Contest, Contested, Contested.

Related words:

Origin: From word contest. Contest is a verb meaning "to dispute," and contestation essentially means "an act, instance, or state of contesting." Both words can be traced to the Latin verb contestari, meaning "to call to witness."

2. Concede (verb): To admit something is true. (स्वीकृति देना)

Synonyms: Admit, Acknowledge, Accept, Allow, Grant, Recognize.

Antonyms: Deny, Disapprove, Refuse, Reject.

Example: After John beat me at chess five times, I had to concede he was the better player.

Verb forms: Concede, Conceded, Conceded.

Related words:

Origin: from Latin concedere, from com- + cedere to yield.

3. Aberration (noun): A departure from what is normal, usual, or expected, typically an unwelcome one.  (पथांतरण /असामान्यता)

Synonyms: Anomaly, Deviation, Divergence, Oddity, Quirk.

Antonyms: Normality, Usualness, Conformity, Regularity.

Example: Shelley’s angry retort was an aberration from her normally quiet demeanor.

Verb forms: Aberrate, Aberrated, Aberrated.

Related words:

Aberrate (verb) - diverge or deviate from the straight path

Origin: from Latin aberrare means ‘to stray’.

4. Reticent (adjective):  Inclined to be silent or uncommunicative in speech/ not revealing one's thoughts or feelings readily.  (मितभाषी/वाक्संयमी)  

Synonyms: Uncommunicative, Reserved, Quiet, Taciturn.

Antonyms: Communicative, Open.

Example: It is okay to be reticent around people you do not know well.

Related words:

Reticence (noun) -  वाक्संयम

Origin:  from Latin reticere,  re- + tacēre to be silent.

5. Prerogative (noun): A right or privilege exclusive to a particular individual or class. (विशेष अधिकर)

Synonyms: Entitlement, Right, Privilege, Advantage

Example: Just because you are rich does not give you the prerogative to break the law!

Related words:

Origin: from Latin praerogativa means privilege.

6. Discretion (noun): The quality of behaving or speaking in such a way as to avoid causing offence or revealing confidential information.  (समझ/बुद्धिमानी)  

Synonyms: Discreetness, Common Sense, Gumption, Prudence, Sensibleness, Wisdom.

Antonyms: Imprudence, Indiscretion.

Example: Since there is a storm overhead, the pilot will depart the airport at his own discretion.

Related words:

Discreet (adjective) – बुद्धिमान

7. Tweak (verb): Improve by making fine adjustments to it.  (सुधारना)  

Synonyms: Adjust, Modify, Alter, Change, Adapt.

Antonyms: Worsen, Aggravate.

Example: He just wanted to tweak his original idea a bit before implementation.  

Verb forms: Tweak, Tweaked, Tweaked.

8. Vagary (noun): An erratic, unpredictable, or extravagant manifestation, action, or notion.  (अनिश्चितताएं)   

Synonyms: Quirk, Idiosyncrasy, Peculiarity, Oddity, Eccentricity, Unpredictability.

Antonyms: Normality.

Example: Because gamblers are familiar with the vagary of the gaming tables, they know luck can change in a hand.

Related words:

Vagarious (adjective) – सनकी

Origin: from Latin vagārī means “to wander, roam”.

9. Caprice (noun): A sudden, impulsive, and seemingly unmotivated notion or action. (सनक)

Synonyms: Whim, Maggot, Megrim, Notion.

Antonyms: Constancy, Stability, Steadiness.

Example: The last time my uncle drank too much whiskey he engaged in a caprice that ended with him spending over a thousand dollars on complete strangers.

Origin: from Italian word capriccio means whim or caprice.

10. Sedition (noun): Conduct or speech inciting people to rebel against the authority   (राजद्रोह/विद्रोह)

Synonyms: Agitation, Revolt, Insurrection.

Antonyms: Obedience.

Example: The newspaper editor was accused of sedition when he encouraged his fans to rise up against government.

Origin: Latin seditio, literally means separation.  sed (apart) + itio (act of going).