5 Things That Annoyed Me This Year

1) Old ladies that must stop right inside the grocery store in front of the exit to look at their damn receipt. Keep walking and check that shit out in your car I’m trying to get somewhere!
2) People that leave 5 car lengths between them and the car ahead of them in the fast lane, when there is no one in the slow lane. Speed up or MOVE OVER.
3) People talking on their cell phone and attempting to drive.
4) Smelly Indians/Middle Easterners. Wear deodorant!
5) Black people who walk slowwww as shit across the parking lot when they see you.
6) Black people thinking they are entitled to acting high and mighty as if they are owed something.
7) Corporate VPs thinking that the rules don’t pertain to them.
8) Annoying cell phone ringers.
9) Slow ass lines when it isn’t even busy at fast food restaurants.
10) People who ask how is married life, and then comment “Let’s see if you are still smiling after a year.” Look… just because you’ve let yourself go and your husband doesn’t want to have sex with you anymore isn’t my problem.
11) People who will smile to your face and stab you in the back.
12) People who can’t be happy for you.
13) Jealous bitches.
14) Woman and how they are so damn moody. Smoke some pot or something.
15) Men that let woman tell them what to do and where, and they listen to it. Get some balls.
16) People who think the rules don’t apply to them.
17) People who always tell you their life story and problems when you didn’t even ask, but then don’t listen to anything you may have to say.
18) Insecure women.
19) People who don’t know the difference between there, their, and they’re.
20) Men who don’t take care of themselves but won’t settle for anything less than a supermodel. It’s called OUT OF YOUR LEAGUE.
21) Loud talkers.
22) Fat woman that comment on my weight, or how I’m losing weight EVERY DAMN TIME I SEE YOU. I haven’t lost a lb in over 5 months.
23) Gay people that cover their car with bumper stickers about abortion and equal rights.
24) Close talkers.
25) People that I don’t even know that well who pick off hair or fuzz from my clothes. 
26) cheap ass horrible smelling perfume.
27) People who talk loud about certain things about their life so everyone can hear how important they really are. NOT.
28) People who don’t think they need to listen to flight attendants. 
29) People who let their kids SCREAM out in public and don’t even try to do anything.
30) Black people who drive BMWs… they think they own the road because they bought a fancy car.
31) People who do EXACTLY the speed limit in the fast lane. MOVE OVER.
32) Women who marry men that are obviously gay…. DUH honey!
33) People who don’t say thank you when you hold the door open for them and just stroll right in like it’s your job to hold the door for them. Well you are welcome your Majesty!
34) Snooty hotel stayers. (“Eh… this isn’t 5star diamond quality, but I guess I’ll have to manage.” Screw you.)
35) People that hold grudges over the dumbest things. 
36) Women who constantly man bash. Why would a man want to be with you anyway if you think so ‘highly’ of them?
37) People who ride their breaks but insist on only keeping 2 inches between them and the car ahead of them.
38) Salesmen.
39) Snooty business people in the airports.
40) Rude help.
41) Passive aggressiveness.
42) Not using car signals.
43) Barking dogs at all hours of the night.
44) cockroaches.
45) People telling me I better hurry up and have kids. Look… I will have kids when I want to have kids!
46) Family drama.
47) Liars.
48) People who you thought were your friends who blow you off for an important event.
49) People who only do things if it benefits them.
50) Down talking.
51) Talking for hours on the phone and you can’t get the person to shut up.
52) Woman who take way too much crap from men and allow them to do so.
53)Screaming kids at the pool when I am trying to relax.
54) Mexican families that house 15 people in an apartment for 2.
55) Illegal aliens that don’t have to pay taxes.
56) Gay marriage. Marriage is between a man and a woman.
57) People who always dodge your call.
58) Co-workers cooking fish and burnt popcorn.
59) People who tell you all about their kids when you never even asked and don’t shut up about them.
60) Woman who constantly seek attention

Don 2 Movie Review

Director: Farhan Akhtar
Cast: Shah Rukh Khan, Priyanka Chopra, Boman Irani

By the time it dawns on you that a 6-feet contemporary Bollywood actor (in a cameo) has been passed off as the unabridged undercover for Shah Rukh Khan's Don in the film, you are expected to be equipped for many more of such cinematic liberties. And rather than crying a spoiler there, you could rather preset your logic mode to the multiple masquerades in store in the movie. 

Don 2, the sequel starts off almost from where the earlier episode ended and while it attempts to maintain some continuity with the last installment, it fails to bring back the intelligence of the original. Don (Shah Rukh Khan) emerges in Malaysia and gets himself arrested only to get the convicted Vardhan (Boman Irani) out of jail. Vardhan has keys to a video footage which they use to blackmail a bank vice president (Alyy Khan) to get access to a German bank's security systems. The big plan is the old-fashioned and formulaic robbery of the currency printing plates from the bank. So the sequel to Don merely boils down to being a heist film.

The film, more or less, starts as an action flick with Don's one-man-army introduction in Thailand, a convenient escape from Malaysian prison and some conventional car-chase sequences in Germany. None of them excite much until you realize you have already reached the interval. The plotting and scheming starts in the second half with an easy induction of a hacker (Kunal Kapoor) who can not only barge into the security systems of the vault but also seems to have blueprints of the bank building to the minutest details.

The writing by Ameet Mehta, Amrish Shah and Farhan Akhtar is more style over substance attempting to camouflage cliches with the cool quotient. Even the central heist seems confusing and convoluted but Farhan Akhtar intentionally keeps the pacing swift enough, leaving no time for the viewer to notice any loose ends. However, the more he makes the situation easy to suit his script, the more it becomes difficult for the audience to digest things.

Even the robbery seems mundane Hollywoodish exercise with no moments of thrills in particular. However the highlight isn't the heist per se but Don's hidden agenda behind it. While it isn't much difficult to decode the mystery, it makes for a decent climax. The director mercifully keeps mush away from the major proceedings though he can't resist the temptation in the climactic portion in his attempts to induce chemistry between Don and his rival, Roma (Priyanka Chopra). But Don would have been better-off as the suave and stonyhearted killer rather than a 'Rahul' prototype. Thankfully the chemistry is peripheral and never blooms into romance.

Also one would have preferred to see Don as more brain over brawny hero but the director makes him a jack of all trades giving him James Bond kinda complete-man characteristics. Vulnerability is alien to Don, essentially making him larger-than-life. But despite being an unethical drug-lord, Farhan Akhtar's treatment is such that you still adore him as the hero over abhorring him as an outright villain. Don 2 never gets into the good v/s evil battle.

The cinematography by Jason West is striking. However Shankar-Ehsaan-Loy's musical score doesn't leave a mark this time and the background score has to repeatedly resort to the theme-piece from the original for some impact. Farhan Akhtar's punch-lines in dialogues are initially amusing but with a Don-ism in every second line, it sounds hackneyed and hollow after a point. 

Shah Rukh Khan is in his comfort zone as the Don bringing more charm than cruelty to his character. He rules supreme and the film's indulgence with him is as much as Don's obsession with himself. Everyone else is overshadowed. Priyanka Chopra is passable. Lara Dutta, as the Don's moll, is simply a substitute for Isha Koppikhar from the prequel and is hardly there for a few scenes. Boman Irani is underused. Kunal Kapoor fails to register any impact. Om Puri, Alyy Khan and Nawab Shah are plain functional. Sahil Shroff irritates.

Don 2 ends with the promise of Don 3 (that's what the number-plate of Don's bike reads) and the trademark dialogue 'Don ko pakadna mushkil hi nahi, namumkim hai' (It's not just difficult to catch don, it's impossible). But we would surely want to 'catch' up with a more worthy sequel to this. It's not impossible Farhan. Is it?

Anna Hazare dubs Lokpal Bill as 'very weak'; dares Sonia Gandhi for public debate

RALEGAN SIDDHI/NEW DELHI: Setting the stage for a confrontation with the Government, Anna Hazare today rejected the Lokpal bill introduced in Parliament, saying it is "very weak" and dared Congress chief Sonia Gandhi for a public debate on the proposed legislation. 

Soon after the bill was introduced in Lok Sabha, Hazare said in Ralegan Siddhi that the new bill is "very weak and useless" and it will not help in tackling corruption as it does not bring CBI under the control of anti-graft ombudsman. 

"This government is incapable of tackling corruption. Why are they scared of giving away CBI? If CBI is under Lokpal's control, they fear that there will be a line of ministers going to jail," Hazare told reporters. 

Hazare said the new Bill is of no use if the anti- corruption ombudsman does not have control over CBI and the lower bureaucracy is not brought under its direct control. 

"Sonia Gandhi says the bill is strong. If it is so, let her come out and debate with us in front of media. Let people see it. Let us have a face to face debate. Convince the people of the country that it is strong. We will explain how it is not strong," he said earlier in the day. 

"What is right and wrong with the bill, let us debate in public," he said. 

Hazare's remarks came as a response to Gandhi's speech at Congress Parliamentary Party meeting yesterday during which she said the proposed legislation was strong and she was ready to fight for it. 

Continuing his attack on the government, Hazare said he will go ahead with his three-day fast from December 27 in Mumbai and then leave for Delhi to join the 'jail bharo' agitation during which he will protest outside the residences of Sonia Gandhi and Rahul Gandhi. 

Describing the bill as "anti-people and dangerous", Hazare's close aide Arvind Kejriwal said in Ghaziabad (UP) it was "worse" than the legislation introduced in August in Lok Sabha.

Corruption: Why Gen X supports Jan Lokpal

Corruption knocks 1.5% off GDP and stories of mega scams abound in the backdrop of people's representatives asking for more perks of office (red light and higher protocol). It also does not help that one-third of the parliamentarians are there because of their families, one-third have criminal records and the remaining one-third possibly cannot be dissociated from chicanery and they will continue to be there so long as elections are like multiple choice tests where citizens will have to choose from all defective answers. 

People see parliamentary performance on television, a Bill gets exactly 10 minutes to be passed in the presence of a 10th of the House. A far cry from debate, discussion and modification on the floor. Even if the debate takes place, the range and the depth are limited, often enough. In this background, beating the chest that Parliament is supreme and the war cry that it is the job of the government to make laws sounds hollow and reflects the hiatus between the people and their representatives. 

Imagine a situation when someone gets a call to come and meet some agent once the passport is made but does not. When she receives a newly-minted passport by courier to discover that it has been deliberately mutilated, anger and anguish are natural. But the difference is that she is not prepared to accept it as the inevitable wheel of life. She understands that the entire chain of corruption is to be countenanced. 

The reluctance to keep CBI's anti-corruption wing under the Lokpal is surprising. The interlocked arrangement and relationship of dependence of the CBI with the government keeps the CBI beyond the realm of impartiality as far as the government is concerned. CBI has got powers but it is not independent. CVC is independent but does have sufficient power and resources. The merger of anti-corruption wings of the government and bringing them under the control of Lokpal is well-thought-out and emerges largely from positive experience of Karnataka.

On bringing the Group C and D employees under Lokpal. Either we accept corruption is a corrosive problem or we do not. If we accept the former is an issue, we will have to recognise the chain and a system is to be devised that will deter corruption by bringing the corrupt to the book and meting out punishment quickly. The argument that a lot of employees are required to cover 57 lakh Group C employees is not convincing. The presence of the law itself will deter the corrupt and make them careful. Perfectlyreasonable people who often descend to corruption in the absence of deterrence are more likely to behave. It will be stupidity to design a system as if everyone is corrupt because given the right climate, majority of them will turn out to be clean. If the need arises to recruit more people, say 10,000 or 20,000, so be it. This is the price the system will have to pay to bring corruption under control. 

Ponting still awaiting 'Tendulkar-like' re-birth

MELBOURNE: In a defiant captain's swansong,Ricky Ponting hit a fighting century in a losing cause as Australia bowed out of the World Cup earlier this year and then spoke of his hopes for a "Tendulkar-like" re-birth. 

Nine months later, the gritty Tasmanian is still gazing at the horizon, waiting for a new dawn that has stubbornly refused to break. 

In Australia's four-Test series against India starting December 26, Ponting will face off once again with the man he desperately wants to emulate. 

Former captains alike and the most prolific run-scorers of all time in Tests and one-dayers, Ponting and Sachin Tendulkar are still two of the brightest stars in cricket's firmament. 

They head into the Boxing Day Test at the Melbourne Cricket Ground both desperate for a century but for very different reasons. 

Tendulkar, afforded God-like status in a nation of a billion people, needs one more to complete his 100th international century, a near-mythical landmark that many doubt will ever be eclipsed. 

Ponting, who stepped down from the captaincy in March and turned 37 on Monday, needs a first Test ton in nearly two years merely to save his career. 

Each have had their chances, with Tendulkar especially tantalising as he reached 94 in the third Test against the West Indies in Mumbai last month before nicking an edge to the slips. 

The 38-year-old also threatened with a 76 in the first West Indies Test following a 91 in the fourth Test against England at the Oval in August. 

He arrives in Australia still near the peak of his powers, having amassed 651 runs in eight Tests for an average of 46.50 this year. 

Ponting, conversely, is a shadow of his former dominant self. Two half-centuries in his last four Tests have lifted his average to a paltry 24.84 for the past year. 

Ponting's recent dismissals, flailing across the crease with the ball invariably cannoning into his pads, have been seen as an indication of a man no longer the master of his technique, let alone the match of the world's best bowlers. 

With debate raging about his place in the team, his captain Michael Clarke has backed him to follow Tendulkar into his own Indian summer - as soon as that elusive third digit again appears next to his name on the scoreboard. 

"Once he makes that score, he'll go on like Sachin and the next few years of his career could be his best," Clarke said before Australia's tour of South Africa last month. 

"Ricky's a huge help to a lot of the young guys in our group, passing on experience and knowledge. I still do a lot of work with him on my batting," he said. 

Ponting and Tendulkar's will undoubtedly loom large in cricket long after they bow out of the game but their careers may be viewed quite differently. 

Tendulkar's legend was born when the curly-haired 16-year-old defiantly batted on with a blood-stained shirt after being struck in the mouth by a Waqar Younis delivery during his 1989 debut in Pakistan. 

His aura only grew from there as he racked up century after century with an effortless grace that Don Bradman remarked was similar to his own. 

Ponting hammered 96 on debut as a 20-year-old against Sri Lanka, and his fiercely competitive nature and front-foot aggression has propelled him to 39 Test centuries and 42 Test wins as captain, the most ever. 

Moulded in a succession of ruthless teams bound by a culture of winning, the belligerent Tasmanian remains a figure of respect rather than adulation in Australia. 

The public is unlikely ever to forgive or forget his crime of captaining the team to a third Ashes series loss earlier this year, and a protracted departure will not help. 

"It is a tough thing to decide when it is the end," former Australia skipper Greg Chappell told local radio this week. 

"The players of Ricky Ponting's calibre are rare and it is better to give them one game or one series too many than one game or one series too few because there aren't that many that can replace them. 

"There does come a point - and I don't want to make a comment one way or another about Ricky's stage - where there is a diminishing return on the investment and the decision has to be taken as to whether there is somebody else who can do as well at the moment but has a chance to get better."

essence of UPSC

essence of UPSC

I want to convey one interesting and importance message.
I watched the movie "Three idiots" and found that it shows the true
path to the UPSC Aspirant.

Amir Khan says that we should not study for scoring the marks only or
mere gathering the information,
main purpose of the study should be enhancing our knowledge, thats why
he says that we can say to the tiger
"well trained" when he jumps on the chair choping with the hunter by
the ring master, but we cannot say him "well educated"

This is the essence of UPSC, what it seeks from the examinee.

UPSC doesn't give marks for mere dipictng the facts or puting the
statistics in the answers.
It expects someting extra from the student when it says in the
questiion "discuss". or "comment" .
There is much diference between the 'Information' and 'Knowledge' .

Most of the questions are of analytical in nature .If it gives one
statment, you have to give your justification in
support of it or against it. For this you must be knowledgeable, you
must develop 360 degree knowledge
of the fact to justyfy  your answer. If you are knowledgeable, you can
give answer of the question an any angle.

So while reading, one must think the all aspect of the fact, it
applicablity, its pros and cons, statistics less matters.
you should have depth of knowledge. We should read not only for
gathering information but also for enhancing our knowledge.
thats why, Mr. Shah Faesal, the IAS topper in 2009 has rightly said
that he had read not for UPSC but for himself.
He wanted to enhance his knowledge .    And what a great man he is !

IT is applicable for every type of questions that UPSC ask in the
examination.

Even in the question of Science and Technology, it does't expect much
in technicality, but how it works, its applicability and its
benifit and future prospects in overall.

What Amir khan says it  absulutely true, if you gain knowledge,
success will follow you, otherwise you will follow the success.
He himself has shown in the end of the movie,  when he is called for
the contract by a man who secure a high profile job
with his socring marks but ultimately comes to Amir Khan to sign
contact for the new project as he is able to do it due to his
inventive knowledge and he is regarded as scientist.

So i wish that every new aspirant should watch this movie and decide
his path of strategy of preperation.

If you gain knowledge, it will be very easy to crack UPSC against what
it is said the tuffest examination.

Shatyam Shivam Sundaram

**********************************************************************************
Shatyam Shivam Sundaram
**********************************************************************************
To start the description about this and to know about this , one needs to be clear of all thoughts , needs to forget everything , everyone and this whole world.To get the real meaning one must think that he is out of every thought , and knows nothing, there is no any power no God and no any work left for him.These things are necessary to understand the power of this phrase as it can change one's life, clear him all from all his sins and when we know all about this phrase we can get a new thinking a new world and a definition for our life.
"Satyam Shivam Sundaram" is not just three words but its three words combining the whole world, its not only saying or uttering of three words but its  a process , a life cycle , a way to live and a way to end. The process of birth to end is controlled by Shatyam Shivam Sundaram , the life starts with...

Satya (Truth): No body knows where we were before birth and where we will go after death , this is the ultimate truth of life , no one knows what made us to have birth, what made us to live and what we will do after death.After having so many thoughts so many brainstormings we say that the death is the ultimate truth. We define death as the truth which all have to face one day , but nobody is capable enough of defining this life , is it a truth or a dream .No life is not a dream or a falsehood and life is not about only a period from birth to death , life is only life when we know what is 'Satya' and what does this 'Satya' means for us. 'Satya' in its purest and pristine form means
the thing you accept by heart , for which you crave , for the one you wait and  the happiness you long for. Everybody finds a truth in his life to be happy  and to add value to his life.When a saint meditates he sees God as his truth , all of his heartily thoughts become pure , he knows no lust for this world , for him as he has got the truth. So the life starts only when we know about our truth and its complete sense. When  a man kills someone he finds his truth in his reasons , he finds the truth if he holds the believe that it was good and reasonable for someone. In married life a wife finds the truth in his husband and husband in his wife ,the wife finds her truth in the happiness of her husband and , she finds the truth in her trust over her husband and she finds the truth in his deeds. For a laborer the truth lies in his labor, he finds the truth in his hunger and in the beauty of work he is doing .So the life starts for them when they find the truth , the Satya for themselves, when their life get a meaning in the form of the Satya they have found.This phase of life moves on to the next stage....shiva

Shiva(The eternal piece of mind):  Shiva means the concentration, the love , the dedication , the commitment , the hunger and the crave for our satya. When we follow the way of our satya forgetting the fact that we are in a body , we are the creatures made of flesh and even forgetting that we have to breath to live. Its the craving to dedicate ourselves to our truth (the satya),its our dedication to be one with our truth ,its the love to being our truth and its the hunger to grow for truth.Shiva means realization of truth in our life and being the truth of our life.To continue with , the saint when he knows that his God is his truth he meditates more and more to be a part of his god , he feels his God , he calls the God as Shiva but he himself is being shiva. It happens the same for the murderer when he finds the truth in his sin , he  becomes shiva with truth as he is loving the truth.If he had not a honest reason for killing then he was a murderer but when an honest and truthful reason is added to his deed then he himself finds the shiva in truth.When he has no reason he will never get the shiva of his life.He can never come out of his guilt.When a hangman (Jallaad) hangs a terrorist then his truth lies in the hanging and he gets the shiva in the thought that his satya his work will give a relief to those thousands who were pained by this man hanged by me.A wife dedicates himself to her husband and the husband to her , for them their love and trust being the ultimate truth , the truth that lies in their pair , the truth that lies in the combined thought of their pair and the truth which results in the deeds of both.They are shiva together , their love for them is satya and the complete mingling of their minds and soul is the shiva.They forget their own bodies ,thoughts and aspirations and they see their shiva in the combined truth of thoughts.The working laborer finds the shiva when he sweats ,when he eats and when he sees his green fields .He weeps on droughts because he looses his wealth but he regains because he holds his satya and shiva. He finds his shiva again in his toil and in his hands when he breaks stones or ploughes the fields. The shiva gives purity to life , adds love , happiness and overall a commitment to life.This shiva on the face of maximas becomes the beauty, becomes the charm and becomes the eternity of happiness which is called Sundaram..

Sundaram(The beauty): When we forget ourselves in shiva, when we submerge in the shiva , the shiva which is a name of god for someone, which is a satisfaction for someone and which is a love for someone.Shiva is not only the name of a God its a word describing a state ,a power, a selfless thought for the all the one who believes in god and and for the one too who does not.
When we feel the presence of shiva , the purity of thoughts , the end of desires and see only the shiva then the life becomes sundaram(beautiful). The one who follows his shiva , the one who is lost in shiva becomes the sundaram.This is the phase where we know the complete truth , follow the truth and be the truth ourselves.To end up with, the saint becomes a truth for his followers and his thoughts ,his words a beauty for this world.His actions become ideals for others.He himself becomes the sundaram , an ideal for others.The murderer , the killer becomes sundar as he gains his truth in deep in his shiva, this is how Bhagat Singh , Hari Singh Nalwa m Ashfaq Ulla Khan and all got their shiva and becomes sundaram for us.The husband-wife couple after forgetting their ownselves become shiva and when they are completely in a combine they are called the sundaram.Their loves becomes a beauty to see ,their love their shiva becomes their soul, their god and their only truth to live.This phase is the utmost beautiful phase for them ,the sundaram for them and from here they will never be different bodies as the combined sould has become the Satyam Shivam Sundaram.Similarly The laborer  walks again after the drought and his labor is the sundaram for his eyes,the green fields and his toil is the beautiful view for all who eat the grains of his field in any form.The food for everyone from his toil and sweat becomes the new truth and the beauty of his thoughts , his toil and we all see the sundaram in his sweat.

In the conclusion no one can say that Satyam Shivam Sundaram ends here only, its just beyond eternal and it will be even there will be no life because truth never dies and the soul of truth the shiva will always be there in the form of any deed followed by satya which will always persist in the nature and will beautify the whole world with sundaram changing lives of someone and giving lives to them who want their satya....

The 3 Greatest Reasons to Move to the Cloud

The 3 Greatest Reasons to Move to the Cloud


I would like to thank one of my readers for asking me what are the 3 greatest reasons a business should move to the cloud.  I have discussed both the benefits and disadvantages of cloud adoption, but it is time to bring some perspective on the matter from the point of view of those who have not yet moved to the cloud.
Obviously, each business has its own priorities and decides what is important, so it is quite a challenge to come up with some criteria that would apply in all situations. However, this is the nature of cloud computing, its characteristics are universally beneficial.
I believe that all businesses could benefit from the advantages below, making it the top 3 greatest reasons for any business to move to the cloud.
Cost: The economic crisis is forcing all businesses to reduce expenses, so this seems to be the most important reason for adopting cloud technologies. There are no upfront investments for hardware and there is the great advantage of only paying for what you use. Cloud computing saves time and money and will also give your business a competitive advantage. Here is an example of how I reduced operational expenses by 30%.
On demand utility: Cloud computing will bring to your business both the efficiency and the flexibility needed in an ever changing economic environment.  It will allow you to focus on your product, processes and services, instead of dealing with IT problems. If your business has specific usage patterns and you only need high resources during limited periods of time, cloud computing is the perfect solution for this type of challenge.
Future:   I already said that cloud computing is a safe bet for the future.  Also, spending on cloud computing technologies will increase 200% by 2015 according to this study. The IT industry, along with software development, is fundamentally changing to adapt to the new technologies. It is time to embrace the future.
What about you? What are the top 3 reasons for your company to move to the cloud?

Knowledge Share: Simple Interest and Compound Interest formulas:

Knowledge Share: Simple Interest and Compound Interest formulas:: Compound Interest formulas: Let Principal = P, Rate = R% per annum, Time = n years.
When interest is compound Annually:
Amount = ...

Simple Interest and Compound Interest formulas:

1. Compound Interest formulas:
   
   
   Let Principal = P, Rate = R% per annum, Time = n years.
2. When interest is compound Annually:

   Amount = P		1 +	R		n
   			100

3. When interest is compounded Half-yearly:

   Amount = P		1 +	(R/2)		2n
   			100

4. When interest is compounded Quarterly:

   Amount = P		1 +	(R/4)		4n
   			100

5. When interest is compounded Annually but time is in fraction, say 3 years.

   Amount = P		1 +	R		3	x		1 +	R
   			100						100

6. When Rates are different for different years, say R₁%, R₂%, R₃% for 1^st, 2^ndand 3^rd year respectively.

   Then, Amount = P

   1 +

   R1

   1 +

   R2

   1 +

   R3

   .

   100

   100

   100

7. Present worth of Rs. x due n years hence is given by:

   Present Worth =	x	.
   	1 + R 100

   
   
   
   Simple Interest:
   
   
   
   
   1. Principal:
      The money borrowed or lent out for a certain period is called the principal or thesum.
   2. Interest:
      Extra money paid for using other's money is called interest.
   3. Simple Interest (S.I.):
      If the interest on a sum borrowed for certain period is reckoned uniformly, then it is called simple interest.
      Let Principal = P, Rate = R% per annum (p.a.) and Time = T years. Then

      (i). Simple Intereest =		P x R x T
      		100

      
      

      (ii). P =

      100 x S.I.

      ; R =

      100 x S.I.

      and T =

      100 x S.I.

      .

      R x T

      P x T

      P x R

Ratio and Proportion

• Compounded Ratio of two ratios a/b and c/d is ac/bd, i.e., ac : bd.
  Duplicate ratio of a : b is a² : b²
  Triplicate ratio of a : b is a³ : b³
  Sub-duplicate ratio of a : b is a : b
  Sub-triplicate ratio of a : b is³a :³b
  Reciprocal ratio of a : b is b : a
• Proportion. Four (non-zero) quantities of the same kind a, b, c, d are in proportion,
  written as a : b :: c : d iff a/b = c/d
• The non-zero quantities of the same kind a, b, c, d, ... are in continued proportion iff
    a/b = b/c = c/d = ...
  In particular, a, b, c are in continued proportion iff a/b = c/d. In this case b is called the mean proportion; b = ac; c is called third proportional. If a, b, c, d are in proportion, then d is called fourth proportional.
• Invertendo. If a : b :: c : d then b : a :: d : c
  Alternendo. 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)
      i.e., a/b = c/d => (a +b)/(a - b) = (c +d)/(c +d)
• If a/b = c/d = e/f = ..., then each ratio = (a +c +e +...)/(b +d +f +...)

Exercise

1. Find the ratio of
   (i) 45 minutes to 5¾ hours
   (ii) 4 months and 2½ years
   (iii) 1·2 kg and 60 gm.
2. Find the compounded ratio of
   (i) 5 : 7 and 9 : 10
   (ii) (x +y) : (x -y) and (x -y) : (x +y)
   (iii) 2a : 3b, 2b : 3a, a² : b²
3. Find the following
   (i) the duplicate ratio of 3 : 7
   (ii) the triplicate ratio of 2 : 5
   (iii) the sub-duplicate ratio of 36 : 25
   (iv) the sub-triplicate ratio of 27 : 1
   (v) the reciprocal ratio of 9 : 11.
4. Find the following
   (i) the duplicatae ratio of 2x : 3y
   (ii) the sub-duplicatae ratio of 16a² : 25b²
   (iii) the sub-triplicate ratio of a⁶ : 8b³
5. Which ratio is greater 17 : 21 or 23 : 28?
6. Arrange the following ratios in descending order of magnitude
      13 : 9, 25 : 23, 16 : 11 and 20 : 17
7. Arrange the ratios 2 : 3, 3 : 4, 4 : 5 in ascending order of magnitude.
8. A man earns Rs 5000 per month and spends Rs 3500 per month. Find the ratio of his
   (i) expenditure to income
   (ii) savings to income
   (iii) savings to expenditure.
9. If A : B = 4 : 5, B : C = 6 : 7, find A : C
10. If A : B = 6 : 7, B : C = 8 : 9, find A : B : C
11. Find the number which bears the same ratio to 7/33 that 8/21 bears to 4/9.
12. Two numbers are in ratio 7 : 11. If 7 is added to each of the numbers, the ratio becomes 2 : 3. Find the numbers.
13. A ratio is equal to 3 : 7. If the antecedent is 5, find the consequent.
14. Find two numbers in the ratio of 8 : 7 such that when each is decreased by 12½, they are in ratio 11 : 9.
15. Divide Rs 170 in the ratio 3 : 7.
16. Find the value of x in the following proportions
    (i) 10 : 35 = x : 42
    (ii) 3 : x = 24 : 2
    (iii) 2·5 : 11·5 = x : 3
    (iv) x : 50 :: 3 : 2.
17. Find the fourth proportional to
    (i) 1/3, 1/4, 1/5
    (ii) 1·5, 2·5, 4·5
    (iii) 9·6 kg, 7·2 kg, 28·8 kg
    (iv) 2xy, x², y²
18. Find the third proportional to
    (i) 5, 10
    (ii) 1·3, 3·9
    (iii) 21/4 and 7
    (iv) x² -y², (x +y)²
    (v) 2 x, 4 x².
19. Find the mean proportion of
    (i) 5 and 80
    (ii) 1/12 and 1/75
    (iii) 8·1 and 2·5
    (iv) 5 +2, 5 -2
    (v) (a -b)³, (a -b)⁵
20. What should be subtracted from 23, 30, 57 and 78 so that the remainders may be in proportion?
21. What number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?
22. Find two numbers such that their mean proportional is 9 and the third proportional is 243.
23. If three quantities are in continued proportion, prove that first is to third is the duplicate ratio of the first to the second.
24. If a  b and a : b is the duplicate ratio of (a +c) and (b +c), prove that c is the mean proportional between a and b.
25. If b is the mean proportional between a and c, prove that
           (a² -b² +c²)/(a^-2 -b^-2 +c^-2) = b⁴
26. If x/a = y/b = z/c, prove that each ratio is equal to 
27. If y is the mean proportional between x and z, prove that xyz(x +y +z)³ = (xy +yz +zx)³.
28. If x/a = y/b = z/c, prove that
    (i) 
    (ii) 
29. If x/(b-c) = y/(c-a) = z/(a-b), prove that
    (i) ax +by +cz = 0
    (ii) x +y +z = 0
30. If ax = by = cz, prove that x²/yz + y²/xz + z²/xy = bc/a² + ca/b² +ab/c²
31. Find x from the following equations:
    (i) [(a +x) +(a -x)]/[(a + x) -(a - x)] = c/d
    (ii) 16

Answers

1. (i) 3 : 23     (ii) 2 : 15       (iii) 20 : 1
2. (i) 9 : 14    (ii) 1 : 1         (iii) 4a² : 9b²
3. (i) 9 : 49     (ii) 9 : 125      (iii) 6 : 5       iv) 3 : 1         (v) 11 : 9
4. (i) 4x : 9y    (ii) 4a : 5b     (iii) a² : 2b.  5. 23 : 28
6. 16 : 11, 13 : 9, 20 : 17, 25 : 23          7. 2 : 3, 3 : 4, 4 : 5
8. (i) 7 : 10      (ii) 3 : 10      (iii) 3 : 7       9. 24 : 25.     10. 48 : 56 : 63
11. 2/11           12. 49 and 77              13. 35/3          14. 40, 35
15. Rs 51, Rs 119     16 (i) 12      (ii) 1/4      (iii) 5      (iv) 75
17. (i) 3/20   (ii) 7·5    (iii) 21·6 kg  (iv) x y/2
18. (i) 20     (ii) 11·7  (iii) 28/3      (iv) (x +y)³/(x-y)     (v) 8 x³
19. (i) 20     (ii) 1/30  (iii) 4·5        (iv) 3                    (v) (a -b)⁴
20. 6            21. 3                         22. 3,27
31. (i) 2acd/(c² +d²)   (ii) a/3