The average of 6 consecutive natural numbers is K. If the next two natural numbers are also included, how much more than K will the average of these 8 numbers be? ?->(Show Answer!)

1. The average of 6 consecutive natural numbers is K. If the next two natural numbers are also included, how much more than K will the average of these 8 numbers be?

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By: anil on 05 May 2019 01.51 am

Let the 6 consecutive numbers be a-3,a-2,a-1,a,a+1,a+2 average = $$frac{SumofElements}{NumberofElements}$$ It is given that average of 6 consecutive numbers be k and hence k = $$frac{a-3+a-2+a-1+a+a+1+a+2}{6}$$ = $$frac{6a-3}{6}$$ = a - $$frac{1}{2}$$ now next two numbers (a+3, a+4) are also added Sum of 8 numbers = a-3+a-2+a-1+a+a+1+a+2+a+3+a+4 = 8a +4 average of 8 numbers = $$frac{8a+4}{8}$$ = a + $$frac{1}{2}$$ = k + 1 so average of 8 numbers is more than average of 6 numbers by = k+1 - K = 1

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MCQ-> Read the following passage carefully and answer the questions given below it. Certain words/phrases have been given in bold to help you locate them while answering some of the questions: In every religion, culture and civilization feeding the poor and hungry is considered one of the most noble deeds. However such large scale feeding will require huge investment both in resources and time. A better alternative is to create conditions by which proper wholesome food is available to all the rural poor at affordable price. Getting this done will be the biggest charity.Our work with the rural poor in villages of Western Maharashtra has shown that most of these people are landless laborers. After working the whole day in the fields in scorching sun they come home in the evening and have to cook for the whole family. The cooking is done on the most primitive chulha (wood stove) which results in tremendous indoor air pollution. 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MCQ-> The second plan to have to examine is that of giving to each person what she deserves. Many people, especially those who are comfortably off, think this is what happens at present: that the industrious and sober and thrifty are never in want, and that poverty is due to idleness, improvidence, drinking, betting, dishonesty, and bad character generally. They can point to the fact that a labour whose character is bad finds it more difficult to get employment than one whose character is good; that a farmer or country gentleman who gambles and bets heavily, and mortgages his land to live wastefully and extravagantly, is soon reduced to poverty; and that a man of business who is lazy and does not attend to it becomes bankrupt. But this proves nothing that you cannot eat your cake and have it too; it does not prove that your share of the cake was a fair one. It shows that certain vices make us rich. People who are hard, grasping, selfish, cruel, and always ready to take advantage of their neighbours, become very rich if they are clever enough not to overreach themselves. On the other hand, people who are generous, public spirited, friendly, and not always thinking of the main chance, stay poor when they are born poor unless they have extraordinary talents. Also as things are today, some are born poor and others are born with silver spoons in their mouths: that is to say, they are divided into rich and poor before they are old enough to have any character at all. The notion that our present system distributes wealth according to merit, even roughly, may be dismissed at once as ridiculous. Everyone can see that it generally has the contrary effect; it makes a few idle people very rich, and a great many hardworking people very poor.On this, intelligent Lady, your first thought may be that if wealth is not distributed according to merit, it ought to be; and that we should at once set to work to alter our laws so that in future the good people shall be rich in proportion to their goodness and the bad people poor in proportion to their badness. There are several objections to this; but the very first one settles the question for good and all. It is, that the proposal is impossible and impractical. How are you going to measure anyone's merit in money? Choose any pair of human beings you like, male or female, and see whether you can decide how much each of them should have on her or his merits. If you live in the country, take the village blacksmith and the village clergyman, or the village washerwoman and the village schoolmistress, to begin with. At present, the clergyman often gets less pay than the blacksmith; it is only in some villages he gets more. But never mind what they get at present: you are trying whether you can set up a new order of things in which each will get what he deserves. You need not fix a sum of money for them: all you have to do is to settle the proportion between them. Is the blacksmith to have as much as the clergyman? Or twice as much as the clergyman? Or half as much as the clergyman? Or how much more or less? It is no use saying that one ought to have more the other less; you must be prepared to say exactly how much more or less in calculable proportion.Well, think it out. The clergyman has had a college education; but that is not any merit on his part: he owns it to his father; so you cannot allow him anything for that. But through it he is able to read the New Testament in Greek; so that he can do something the blacksmith cannot do. 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In other words, if the blacksmith is to have a shilling, is the parson to have six pence, or five pence and one-third, or two shillings? Clearly these are fools' questions: the moment they bring us down from moral generalities to business particulars it becomes plain to every sensible person that no relation can be established between human qualities, good or bad, and sums of money, large or small.It may seem scandalous that a prize-fighter, for hitting another prize-fighter so hard at Wembley that he fell down and could not rise within ten seconds, received the same sum that was paid to the Archbishop of Canterbury for acting as Primate of the Church of England for nine months; but none of those who cry out against the scandal can express any better in money the difference between the two. Not one of the persons who think that the prize-fighter should get less than the Archbishop can say how much less. What the prize- fighter got for his six or seven months' boxing would pay a judge's salary for two years; and we all agree that nothing could be more ridiculous, and that any system of distributing wealth which leads to such absurdities must be wrong. But to suppose that it could be changed by any possible calculation that an ounce of archbishop of three ounces of judge is worth a pound of prize-fighter would be sillier still. You can find out how many candles are worth a pound of butter in the market on any particular day; but when you try to estimate the worth of human souls the utmost you can say is that they are all of equal value before the throne of God:And that will not help you in the least to settle how much money they should have. You must simply give it up, and admit that distributing money according to merit is beyond mortal measurement and judgement.Which of the following is not a vice attributed to the poor by the rich?
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In short, one might argue that culture is the intervention of human effort in refining and redefining that which is natural, but that it gradually takes on other dimensions in the life of the individual, and even more in the interface between the individual and society. When speaking of society, this word also requires defining. Society, it has been said, is what emerges from a network of interactions between people that follow certain agreed upon and perceptible patterns. These arc determined by ideas of status, hierarchy and a sense of community governing the network. They are often, but not invariably, given a direction by those who control the essentials in how a society functions, as for instance, its economic resources, its technology and its value systems. The explanation and justification for who controls these aspects of a society introduces the question of its ideology and often its form. The resulting patterns that can be differentiated from segment to segment of the society are frequently called its cultures. Most early societies register inequalities, The access of their members to wealth and status varies. The idea of equality therefore has many dimensions. All men and women may be said to be equal in the eyes of god, but may at the same time be extremely differentiated in terms of income and social standing, and therefore differentiated in the eyes of men and women. This would not apply to the entire society. There may be times when societies conform to a greater degree of equality, but such times may be temporary. It has been argued that on a pilgrimage, the status of every pilgrim is relatively similar but at the end returns to inequalities. Societies are not static and change their forms and their rules of functioning. Cultures are reflections of these social patterns, so they also change. My attempt in this introduction is to explain how the meaning of a concept such as culture has changed in recent times and has come to include many more facets than it did earlier. What we understand as the markers of culture have gone way beyond what we took them to be a century or two ago. Apart from items of culture, which is the way in which culture as heritage was popularly viewed, there is also the question of the institutions and social codes that determine the pattern of living, and upon which pattern a culture is constructed. Finally, there is the process of socialization into society and culture through education. There is a historical dimension to each of these as culture and history are deeply intertwined. There is also an implicit dialogue between the present and the past reflected in the way in which the readings of the past changed over historical periods. Every. society has its cultures, namely, the patterns of how the people of that society live. In varying degrees this would refer to broad categories that shape life, such as the environment that determines the relationship with the natural world, technology that enables a control over the natural world, political-economy that organizes the larger vision of a society as a community or even as a state, structures of social relations that ensure its networks of functioning, religion that appeals to aspirations and belief, mythology that may get transmuted into literature and philosophy that teases the mind and the imagination with questions. The process of growth is never static therefore there are mutations and changes within the society. There is communication and interaction with other societies through which cultures evolve and mutate. There is also the emergence of subcultures that sometimes take the form of independent and dominant cultures or amoeba-like breakaway to form new cultures. Although cultures coincide with history and historical change, the consciousness of a category such as culture, in the emphatic sense in which the term is popularly used these days, emerges in the eighteenth century in Europe. The ideal was the culture of elite groups, therefore sometimes a distinction is made between what carne to be called 'high culture' that of the elite, and low culture' that of those regarded as not being of the elite, and sometimes described as 'popular'. Historical records of elite cultures in forms such as texts and monuments for instance, received larger patronage and symbolized the patterns of life of dominant groups. They were and are more readily available as heritage than the objects of the socially lower groups in society whose less durable cultural manifestations often do not survive. This also predisposed people to associate culture as essentially that of the elite.What is the central idea of the passage?
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