Friday, 21 April 2017

Calculation Tricks VII – Multiplying Numbers with Numbers from 11- 19

Calculation Tricks are your best allies when it comes to multiplying numbers in SBI PO, IBPS and SSC CGL Exam and getting to the correct answer in the least amount of time possible.

Multiplying Numbers
Questions in the Quantitative Aptitude section of all competitive exams like SBI PO, IBPS, SSC CGL  not only need you to have strong but also have some calculation tricks up your sleeve, that help you save time. If you are one of those who skips a question just because it needs you to multiply then this calculation trick is especially for you!
So here is the 7th calculation trick and we’ll once again discuss a short cut about multiplying numbers. This trick will make sure that you are able to multiply numbers with numbers from 11- 19. 
Multiplying Numbers

Multiplying Numbers

Ok! now before you rush to kill us for explaining what you were taught in 3rd grade in school let us  tell you why exactly we are discussing about multiplying numbers!  Certainly no question in any competitive exam will directly ask you to multiply two numbers but almost every other question will have you to multiplying numbers with numbers that lie between 11- 19.

Example of Multiplying Numbers from 11 to 19 with the Given Number

What is the answer for-
(i) 1732 x 11     (ii) 1598 x 12     (iii) 38916 x 14      (iv) 43172 x 19

A. 19882, 18176, 444824, 920268
B. 17992, 20176, 644734, 720268
C. 19052, 19176, 544824, 820268
D. 18052, 21176, 588424, 840268

Conventional Method of Multiplying Numbers from 11 to 19 with the Given Number

So what is your usual reaction on reading a question like this? You first multiply 1732 with 11 using the regular method where 1 is first multiplied with 2, then with 3, then 7 and so on… then you go to the next line, and start multiplying 1732 with 1 once again. Only this time you write the numbers in the tens place then add them and get your answer. You follow this method for multiplying all the numbers!
Multiplying Numbers
Multiplying Numbers
Multiplying Numbers
Multiplying Numbers

Smart Method of Multiplying Numbers from 11 to 19 with the Given Number

Let’s simplify this very complicated method of multiplying numbers for you and also help you save some time in the process.
1732 x 11
Step 1:
Multiply the number in the units place with the other number in the units place. In this case multiply 1 with 2
Multiplying Numbers
Step 2:

For the second digit, multiply 1 with 3 and add the previous digit that is 2 in this case, so it will be 5 
Multiplying Numbers

Step 3:

Move on with the remaining digits multiplying with 1 and adding the previous digit in the same way. In case there is a two digit number, carry it forward and add it.
Multiplying Numbers

Let’s try multiplying next two numbers – 1598 x 12
Step 1:
Multiply the number in the units place with the other number in the units place. In this case multiply 2 with 8
Multiplying Numbers

Step 2:
Now in this case 1 will be carried forward. We’ll multiply 2 with 9, and add 8 to it. We get 26, to this we will add the carried forward 1 and so we get 27. Now 7 will be written and 2 will be carried forward.
Multiplying Numbers
Step 3:
Similarly carry on with the entire number and you’ll get the answer.
Multiplying Numbers

Isn’t this way more simple and quick! This method can be used for multiplying numbers from 11 to 19 by this method.

Use this calculation trick while multiplying numbers now-
Question 1: 34568 x 19 = ?
1) 656792      2) 566792      3) 700792     4) 665792

Question 2: 76432 x 13 = ?
1) 993116      2) 993616      3) 100616      4) 103116

Do tell us in the comments section how long you took in multiplying these numbers.

 Multiplying Numbers
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Calculation Tricks VI – Multiplication Tricks to Multiply Numbers with 25

Multiplication Tricks are very handy in SBI PO, IBPS and SSC CGL Exams because they speed up your calculations and save time in competitive exams. Multiplying Numbers will never be the same with these calculation tricks.

Multiplication Tricks
Name any competitive exam… SBI PO, IBPS, SSC Exam, InsuranceExams, Railway Recruitment Board Exams… Irrespective of the name of the exam that you are appearing for, multiplying numbers is a task you cannot run from. Calculation tricks especially multiplication tricks are therefore a basic need in all competitive exams.  We all know that multiplication amongst big numbers can not only be quite a challenge but also be very time consuming. And time is definitely not your friend in such exams.
So in this series dedicated to Calculation Tricks we have discussed some really time effective ways to do calculations. Read on to get some multiplication tricks up your sleeve. This trick will help you in multiplying numbers with 25.
Calculation Tricks

Why do you Need Multiplication Tricks?

Almost every second question in the Quantitative Aptitude Section of SBI PO, IBPS and SSC CGL Exam has you multiplying numbers. Therefore it becomes almost imperative that you have skills that help calculate accurately and quickly. And expertise in multiplying numbers using multiplication tricks can come very handy and help you get closer to the cut off. Here we will discuss multiplying numbers with 25.

A Question where Multiplication Tricks help Multiplying Numbers with 25

436x 25 = ?
1) 15600      2)10900      3)13400      4) 14600      5) None of these

Conventional Method of Multiplying Numbers with 25

How you do normally do you multiply these two numbers? Get a pen and paper, quickly scribble some numbers, do some multiplication with 5 and 2 respectively, then do some addition and then finally you get your answer!
Multiplication Tricks
Undoubtedly this answer is correct and follows the method we were taught in school but what you forget is that multiplying numbers like this also takes 10 seconds!


Smart Method Using Multiplication Tricks

Time to upgrade and use some multiplication tricks that help you complete this calculation quicker and faster! Some multiplication tricks that will not need you to use pen and paper but just reach the answer verbally!
Multiplying numbers with 25 can be done by just substituting 25 with 100/4. So all you need to do is divide the given number by 4 and multiply that number with 100, which is just adding 2 zeros to get the answer.

Step 1:
436 x 25= 436 x (100/4)

Step 2:
 (436/4) x 100= 109 x 100 = 10900
Multiplication Tricks
We all know the table to 4 really well and this calculation is just like mental math! Simple! Quick! Easy!
Practice these questions with multiplication tricks-
Question 1: 1234 x 25 = ?
1) 30850      2)34400      3)31700      4) 37700      5) None of these

Question 2: 6317 x 25 = ?
1) 150345      2)188575      3) 121485      4) 156855      5) 157925

Do write in the comments section below how much time these multiplication tricks helped you save!

Stay tuned for the next trick in the series!
Multiplication Tricks

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Interest III - Problems on Varying Rates of Interest and Difference between Compound Interest and Simple Interest.

In this post, problems are solved based on Varying Rates of Interest and Difference between Compound Interest and Simple Interest in just a couple of steps.

Compound Interest formula and Simple Interest

In our previous post How to find Simple Interest and Compound Interest in the SBI PO, IBPS exam we solved questions using smart methods to save time. This post is divided into two parts - Module 3 and Module 4. Module 3 is based on the problems which have Varying rates of Interest and Module 4 is based on the Difference between Compound Interest and Simple Interest.
Compound Interest formula and Simple Interest
Module 3: Varying Rates of Interest

Do problems on Varying rates of Interest scare you? Do you often think of skipping the problem? Stop worrying. Here are few smart methods which will help you to solve questions in less than 25 seconds. 

Example 1: Varying Rates of Interest


Problem: If 20000 is given as loan for a period of 3 years with the interest rates 5%, 7% and 9% for the 1st, 2nd and 3rd year respectively. What is the total amount that has to be paid at the end of 3 years?

Regular Method

Solution:
Step 1:
  P - 20000
  R - 5%, 7% and 9%
  T - 1, 2 and 3 years i.e 3 years.
  S - ?
  A - ?
Step 2:
  SI = PTR/100
  SI = PTR/100 + PTR/100 + PTR/100 (In case of varying rates of Interest)
  SI = P(TR/100 + TR/100 + TR/100)
  SI = 20000( 1x 5/100 + 1x7/100 + 1x9/100)
  SI = 2000 x 21/100
  SI = 4200
Step 3:
   A = P + SI
   A = 20000 + 4200
   A = 24200.
Therefore, The amount that has to be paid end of three years is Rs.24200/-

Smart Method
The problem is solved using Percentage and Ratio of Equivalent Proportionality.
As this is a case of Simple Interest we add 5% + 7% + 9% [different Rate of Interest for 3 years]  i.e. 21%. Amount here is Principal + Rate of Interest. Principal is 100% of the amount. So, 
   Amount = 100% + 21%. 
  Therefore Amount = 121%

Step 1:                                                                                                                             

As per the Ratio of Equivalent Proportionality we cross multiply the percentage with Principal amount and Principal Percentage with unknown amount to find the actual amount.
                                          Compound Interest formula and Simple Interest
By cross multiplication we get,
     A = (121 x 20000)/100)
     A = 24200
Therefore, the amount that has to be paid end of 3 years is Rs.24200/-

Example 2: Module 3-Varying Rates of Interest


Problem: An amount of Rs.10000 is taken as loan by Vivek at compound interest charging 5% for the first year,10% for the second year and 20% for the third year. What is the total interest to be paid by Vivek at the end of the third year?

Regular Method

Solution:
Step 1:
   P - 1000
   R - 5%, 10%, 20%
   T - 1, 2, 3 years i.e. 3 years.
   CI - ?
Step 2:
   A = p[(1+R1)T1 (1+R2)T2(1+R2)T3
   A = 10000 [(1+5)/100 x (1+10)/100 x (1+20)/100]
   A = 10000 [ (105/100) x (110/100) x (120/100)]
   A = 13860
Step 3:
   CI = A - P
   CI = 13860 - 10000
   CI = 3860
Therefore, Compound Interest for the three years is Rs.3860/-

Smart Method

Solution:
We can solve this problem in just one step by using Effective percentage method and the concept of Ratio and Equivalent Proportionality.
  • First, we need to find the percentage of Compound Interest for the consecutive 3 years by using effective percentage method. 
Effective Percentage of first 2 years.

(a + b + ab)/100

a = 5
b = 10

    5 + 10 +[(5+10)/100]=

15.5%
Effective Percentage of first 2 years Interest+3rd years percentage.



(a + b + ab)/100)


a = 15.5
b = 20


15.5 + 20 +[(15.5+20)/100]=


38.6%
 Compound Interest = 38.6%

Step 1:
By using the concept of Ratio and Equivalent Proportionality we cross multiply Principal Amount with Interest Percentage and Principal Percentage with the unknown amount of Compound Interest to find the Compound Interest paid at the end of 3 years.
                
Compound Interest formula and Simple Interest
Compound Interest = 3860
Therefore, Compound Interest for the 3 years is Rs.3860/-

Module 4: Difference between Simple Interest and Compound Interest
Problems on Difference between Compound Interest and Simple Interest are complex. Solving them by the regular method takes long. The complexity arises due to not having a thorough understanding about the concept. This module deals with the concept of Difference between Simple Interest and Compound Interest using smart method which helps you to pick up your speed during exam and saves time.

Concept:

Let the difference between simple interest and compound interest for a period of T years at the R% p.a be 'D', then the principal P is given as.
Compound Interest formula and Simple Interest
Compound Interest and Simple Interest Formula
*Note: D is the difference between SI and CI.
We can solve problems on this concept by simple substituting the values in the formulas. 

Example 1: Module 4- Difference between Simple Interest and Compound Interest

Problem: Find the difference between Simple Interest and Compound Interest at 5%p.a for two years on a principal of Rs.2000.

Regular Method
Solution:
Step 1:
   P =  2000
   R =  5%p.a
   T =  2 years
   D =   ?
 Step 2:
    P =  D x 1002/R2  
    2000 = D x 1002/52
     D = 5
Therefore, difference between Compound Interest and Simple Interest is Rs.5

Smart Method
Solution:
Step 1:
    SI = 5 + 5 ( rate of interest of two years)                                        
        = 10%
Step 2:
   Compound Interest = 5 + 5 + (5 x 5)/100
                                   = 10.25%
Step 3:
   Compound Interest -Simple Interest             
   10.25% - 0.5% = 0.25%
                  
Step 4:
   Cross multiplication,
                                      Compound Interest formula and Simple Interest
Therefore, difference between Compound Interest and Simple Interest is Rs.5/-

We can easily avoid step one and two by doing the calculation in our mind.

Alternatively, we know that the actual difference between CI and SI is 5 x 5/100 so we can calculate that by directly cross multiplying and avoid step 1 and step 2.

Example 2: Module 4- Difference between Simple Interest and Compound Interest

Problem: If the difference between simple interest and compound interest on some amount at 20 p.a for 3 years is Rs.48, then what must be the principal amount.

Regular Method

Solution:
Step 1:
   P = ?
   D= 48
   R = 20
   T = 3
 Step 2:
    P = D x 1003/R2(300+R)
   P = 48 x 1003/202(300+20)
 Step 3:
    P = 300/8
    P =  375
 Therefore, the Principal amount is Rs.375/-

Solving this problem about the consecutive 3 years difference between Compound Interest and Simple Interest by percentage method is a tedious job. However, the Regular method i.e Substituting values in the formulas is the simplest way to solve this problem. 

Stay tuned for our next post on How to Calculate Interest Compounded Half-yearly. 

Do write in the Comments section on how this blog helped you to break the complexity of the problems.  

Compound Interest formula and Simple Interest




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Daily Update On Current Affairs - April 21, 2017

current affairs
Here's your daily summary of Current Affairs.

ISRO To Test Launch GSLV-Mk III-D1 In May 2017


ISRO is all set to undertake the first developmental flight of a ‘game-changer’ rocket (launching vehicle) that will have the capacity to launch the four-tonne class of satellites, from Sriharikota spaceport. ISRO looks forward to conducting the second developmental flight within this year. 

Significance: With the successful test launch, ISRO can carry out all the launches within the country instead of depending on international agencies for the launch of heavier satellites. Hence, the successful test launch will help in reducing ISRO’s dependency on international launching vehicles. ISRO’s launch vehicles as of now have the capability to launch satellites only up to 2.2 tonne. For the launch of heavier satellites, it had to depend upon the international agencies.  So, the ISRO rightly views operationalisation of this rocket as a “game-changer” mission.

RGIA Gets Carbon Neutrality Status

The Rajiv Gandhi International Airport (RGIA) at Shamshabad has been given the carbon neutrality status by Airports Council International (ACI) under its Airport Carbon Accreditation programme. The airport’s operator GMR Hyderabad International Airport Ltd (GHIAL), a GMR Group-led consortium, has stated that it was conferred with the carbon neutrality (level 3: neutrality) by the ACI at a ceremony held in Doha, Qatar. 

The ACI Airport Carbon Accreditation programme was initiated in June 2009 and consists of four levels: 
Level 1: Mapping
Level 2: Reduction
Level 3: Optimisation
Level 3+: Neutrality

RGIA achieved levels one and two in 2012. It achieved level 3 status in 2013. The level 3+ status which it has achieved now is the fourth and highest accreditation under ACI’s Carbon Accreditation programme. RGIA adopted many sustainable measures like proactive energy conservation, generation of renewable energy, carbon sinking through extensive greenbelt and various other environment protection initiatives to achieve this status. ACI Airports Council International (ACI) is the only global trade representative representing the world’s airport authorities. It is a member of Air Transport Action Group (ATAG). It was established in 1991 and develops standards, policies and recommended practices for airports. The global body represents the interests of airports with governments and international organisations.

Haryana Extends Accidental Insurance Cover To All Citizens


The Pradhan Mantri Bhima Suraksha Yojna has been implemented by the Haryana Government. The scheme is available for one year and subject to renewal thereafter. The scheme covers both accidental death and disability. The cover for accidental death will be Rs 2 lacs and for disability, it will be Rs 1 lac. The scheme is available to all the citizens within the state between the ages of 18 and 70, provided they have an Aadhar card linked bank account. An annual premium of Rs 12 will be deducted from the citizen’s Savings Bank account for this purpose.

Government Sells Stake In NALCO


The government today raised 1,200 crore rupees through the sale of 9.2 percent stake in National Aluminum Company Ltd, NALCO. In the disinvestment, the offer for sale was pegged at 5 percent of paidup capital, but seeing the overwhelming response from the market, the government exercised the option to retain over-subion and raised the offer to 9.2 percent yesterday. With this transaction, the Government's shareholding in NALCO has come down to 65.37 percent.

Supreme Courts Allows Auction Of Taj Mansingh Hotel In Delhi

The Supreme Court has allowed e-auction of five-star hotel Taj Mansingh in Delhi. The hotel is presently being run by a Tata Group firm. The court allowed the plea of New Delhi Municipal Council, NDMC, that the Tata Group firm cannot have the right to refusal in the auctioning of the hotel. The bench, however, asked NDMC to grant six months breathing time to the company in vacating the hotel in case they lose out in the e-auction

EPF Interest Rate Approved At 8.65 %

Labour Minister Bandaru Dattatreya has said that the Finance Ministry has approved 8.65 percent interest rate on EPF for 2016-17. He said the government will immediately issue a notification in this regard. The ratification will enable the retirement fund body EPFO to credit this rate of return into the accounts of  over four crore subscribers. The Employees' Provident Fund Organisation trustees had approved 8.65 percent rate on EPF in December last year.

India Develops National Action Plan To Combat Antimicrobial Resistance

Union Minister of Health and Family Welfare announced the finalization of India’s comprehensive and multi-sectoral National Action Plan at the ‘Inter-Ministerial Consultation on AMR containment’ held at New Delhi. The consultation was attended by various ministers including Minister of Consumer Affairs, Food and Public Distribution Ram Vilas Paswan, and Minister of Environment, Forest and Climate Change Anil Madhav Dave. The Ministers signed a ‘Delhi Declaration’ to contain Antimicrobial Resistance (AMR). The Delhi Declaration calls for the support of all stakeholders including UN, WHO, FAO and other UN agencies, civil society organizations etc., in developing and implementing the national and state action plans on AMR. The National action plan has objectives of enhancing awareness, strengthening surveillance, improving rational use of antibiotics, reducing infections and promoting research

LHS 1140b: Another Planet In Habitable Zone Discovered


Astronomers have discovered yet another planet, called LHS1140b, which is expected to be present in the Goldilocks Zone. It’s not so far away, either. It is found orbiting around the star LHS 1140 some 39 light-years away. Goldilocks Zone refers to a habitable zone where the temperature is neither too high nor too low. The planet is found to be rocky, like the Earth but is over six times as massive as Earth and about 1.5 times larger and falls under the category of ‘Super Earth’. Its gravitational pull will be three times stronger than that of the Earth. Rocky planets within the habitable zone are the best candidates to find evidence of some form of life.


Australia Makes Sweeping Changes To Citizenship Law

Australian Prime Minister Malcolm Turnbull has made sweeping changes to Citizenship laws unveiling tighter requirements for new applicants. This announcement follows the recent scrapping of the 457 visa program for foreign workers, which was used majorly by the Indians. The 457 programme was scrapped to tackle the growing unemployment in the country.

India Contributes USD 2,50,000 To Election Assistance Division Of UN

India has contributed USD 2,50,000 to the UN Election Assistance Division to help other countries to hold elections and develop their electoral systems. This is the second time that India has contributed USD 2,50,000 towards electoral assistance and capacity building. The first assistance was made in 2012.

UNESCO’s Felix Houphouet-Boigny Peace Prize 2017 Winners

UNESCO has named Giuseppina Nicolini, Mayor of Lampedusa (Italy) and the non-governmental organisation SOS Méditerranée (France) as the winners of Felix Houphouet-Boigny Peace Prize 2017 “for their work to save the lives of refugees and migrants and welcome them with dignity”. In the past, Felix Houphouet-Boigny Peace Prize has been granted to internationally renowned personalities like Nelson Mandela, Yasser Arafat, King Juan Carlos of Spain, former US president Jimmy Carter and Shimon Peres. For the first time, the award goes to a mayor.

Auction Of Gandhi Stamps Fetches 500,000 Pounds

A set of four rare Postal Stamps featuring Mahatma Gandhi has fetched an astonishing sum of 500,000 pounds at an auction held in England. The stamps were bought by an Australian collector. As per the records, only 13 of these 1948 Gandhi Rs10 Purple Brown and Lake Service stamps are in circulation now. Apart from this set of four, the other set of four is in the Royal Philatelic Collection, owned by Queen Elizabeth II.


Video Gaming To Be Featured As A Full Sport At The 2022 Asian Games

The Olympic Council of Asia (OCA) will feature Video Gaming as a full sport at the 2022 Asian Games. According to OCA, the decision to include e-sports was taken to reflect “the rapid development and popularity of this new form of sports participation among the youth.” Hence, e-sports would be introduced as a medal sport to the official program of the Asian Games at Hangzhou, China. It will be included as a demonstration sport at the 2018 Asian Games in Palembang, Indonesia. OCA has entered into a collaboration with Alisports, a unit of China’s Alibaba Group, to bring e-sports to the games. However, no details have come out on the details of the video games that would be included. The Asian Games features a wide range of traditional Olympics. It includes some of the more obscure sports like sepak takraw ( a game that has features of soccer and volleyball), kabaddi, etc. It also includes a variety of martial arts, contract bridge, jet-ski racing and sport climbing etc.

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