In a mixture, unbroken and broken rice grains are in the ratio 3 : 2. How much fraction of the mixture must be drawn off and substituted with broken grains, so that the ratio of unbroken and broken grains becomes 1 : 1? ?->(Show Answer!)

1. In a mixture, unbroken and broken rice grains are in the ratio 3 : 2. How much fraction of the mixture must be drawn off and substituted with broken grains, so that the ratio of unbroken and broken grains becomes 1 : 1?

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By: anil on 05 May 2019 02.04 am

Let quantity of unbroken and broken rice grains be $$3$$ and $$2$$ units respectively. Let $$x$$ units of mixture is taken out => Unbroken rice grains in $$(5-x)$$ units of mixture = $$frac{3}{5}(5-x)$$ Similarly, after adding broken rice grains, => Broken rice grains in mixture = $$frac{2}{5}(5-x)+x$$ According to ques, => $$frac{frac{3}{5}(5-x)}{frac{2}{5}(5-x)+x}=frac{1}{1}$$ => $$3-frac{3}{5}x=2-frac{2}{5}x+x$$ => $$frac{3x}{5}-frac{2x}{5}+x=3-2$$ => $$frac{6x}{5}=1$$ => $$x=frac{5}{6}$$ $$ herefore$$ Required fraction = $$frac{frac{5}{6}}{5}=frac{1}{6}$$ => Ans - (B)

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MCQ-> Read the following passage carefully and answer the question given below it.Certain words/phrases have been printed in bold to help you locate them while answering some of the questions.Once upon a time a dishonest King had a man call the Valuer in his court. The Valuer set the price which ought to be paid for horses and elephants and the other animals.He also set the price on jewellery and gold.and things of that kind.This man was honest and just and set the proper price to be paid to the owners of the goods.The King however was not pleased with this Valuer because he was honest ‘If I had another sort of a man as Valuer I might gain more riches, he thought One day the King saw a stupid miserly peasant come into the place yard.The King sent for the fellow and asked him if he would like to be Valuer.The peasant said he would like the position.So the King had him made Valuer He sent the honest Valuer away from the place.Then the peasant began to set the prices on horses and elephants upon gold and jewels.He did not know their value so he would say anything he chose.As the King had made him Valuer the People had to sell their goods for the price he set. By and by a horse-dealer brought five hundred horses to the court of this King.The Valuer came and said they were worth a mere measure of rice and the horses to be put in the palace stables. The horse-dealer went then to see the honest man who had been the Valuer and told him what had happened.’What shall I do ?’ asked the horses-dealer “I think you can give a present to the Valuer which will make him “Go to him and give him a fine present then say to him You said the horses are worth a measure of rice,but now tell what a measure of rice is worth ! Can you value that standing in your place by the King ?’ If he says he can go with him to the King and I will be there too” The horses-dealer thought this was a good idea.So he took a fine present to the Valuer and said what the other man had told him to say.The stupid Valuer took the present,and said,”Yes, I can go before the King with you and tell what a measure of rice is worth.I can go before the King with you and tell what a measure of rice is worth. I can value now. Well let us go at once” said the horses-dealer.So they went before the king and his ministers in the palace.The horses-dealer bowed down before the King and said “O King I have learned that a measure of rice is the value of my five hundred horses.But will the King be pleased to ask the Valuer what had happened asked,How now Valuer what are five hundred horses worth ? “A measure of rice O King !” said he “very good then ! If five hundred horses are worth a measure of rice what is the measure of rice worth ?” The measure of rice is worth your whole city” replied the foolish fellow The minister clapped their hands laughing and saying “What a foolish Valuer! How can such a man hold that office ? We used to think this great city was beyond price but this man says it is worth only a measure of rice.Then the King was ashamed and drove out the foolish fellow “I tried to please the King by setting a low price on the horses and now see what has happened to me !’ said the Valuer as he ran away from the laughing crowd.Who did the King appoint as the new Valuer ?
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MCQ-> Read the following passage carefully and answer the question given below it.Certain words/phrase have-been printed in the bold to help you locate them while answering some of the questions. King Hutamasan felt he had everything in the world not only due to his riches and his noble knights but because of his beautiful queen Rani Matsya The rays of the sun were put to shame with the iridescent light that Matsya illuminated with her beauty and brains At the right hand of the king she was known to sit and aid him in all his judicial probes You could not escape her deep-set eyes when you committed a crime as she always knew the and the culprit Her generosity preceded her reputation in the kingdom and her hands were always full to give people in the kingdom revered her because if she passed by she always gave to the compassionate and poor Far away from the kingly palace lived a man named Raman with only ends to his poverty as he had lost all his land to the landlord,His age enabled him little towards manual labour and so begging was the only alternative to salvage his wife and children Every morning he went door to door for some work food or money.The kindness of people always got him enough to take home But Raman was a little self centered His world began with him first followed by his family and the rest So he would eat and drink to his delight and return home with whatever he found excess This routine followed and he never let anyone discover his interest as he always put on a long face when he reached home. One day as he was relishing the bowl of rice he had just received from a humble home he heard that Rani Matsya was to pass from the very place he was standing Her generosity had reached his ears and he knew if he pulled a long face and showed how poor he was she would hand him a bag full of gold coins enough for the rest of his life enough to buy food and supplies for his family.He thought he could keep some coins for himself and only reveal a few to his wife so he can fulfill his own wishes. He ran to the chariot of the Rani and begged her soldiers to allow him to speak to the queen Listening to the arguments outside Rani Matsya opened the curtains of her chariot and asked Raman what he wanted Raman went on his knees and praised the queen I have heard you are most generous and most chaste show this beggar some charity Rani narrowed her brows and asked Raman what he could give her in return Surprised by such a question Raman looked at his bowl full of rice With spite in him he just picked up a few grains of rice and gave it to the queen Rani Matsya counted the 5 grains and looked at his bowl full of rice and said you shall be given what is due to you Saying this the chariot galloped away Raman abused her under his breath This he never thought would happen How could she ask him for something in return when she hadn’t given him anything ? Irked with anger he stormed home and gave his wife the bowl of rice Just then he saw a sack at the enterence His wife said some men had come and kept it there He opened it to find it full of rice He put his hand inside and caught hold of a hard metal only to discover it was a gold coin Elated he upturned the sack to find 5 gold coins in exact for the five rice grains If only I had given my entire bowl thought Raman I would have had a sack full of gold.According to the passage which of the following is definitely true about Rani Matsya ? (A)She was beautiful (B)She was intelligent (C)She was kind....

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. 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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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