LINEAR EQUATION PROBLEMS FOR VYOM 

1. If you subtract 1 2 from a number and multiply the result by 1 2 , you get 1 8 . What is the number?

2. The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?

3. The base of an isosceles triangle is 4 cm 3 . The perimeter of the triangle is 2 4 cm 15 . What is the length of either of the remaining equal sides?

 4. Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

5. Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?

6. Three consecutive integers add up to 51. What are these integers?

 7. The sum of three consecutive multiples of 8 is 888. Find the multiples.

8. Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.

9. The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?

10. The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?

11. Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?

12. Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age?

 13. A rational number is such that when you multiply it by 5 2 and add 2 3 to the product, you get 7 12 − . What is the number?

 14. Lakshmi is a cashier in a bank. She has currency notes of denominations Rs 100, Rs 50 and Rs 10, respectively. The ratio of the number of these notes is 2:3:5. The total cash with Lakshmi is Rs 4,00,000. How many notes of each denomination does she have?

15. I have a total of Rs 300 in coins of denomination Re 1, Rs 2 and Rs 5. The number of Rs 2 coins is 3 times the number of Rs 5 coins. The total number of coins is 160. How many coins of each denomination are with me?

16. The organisers of an essay competition decide that a winner in the competition gets a prize of Rs 100 and a participant who does not win gets a prize of Rs 25. The total prize money distributed is Rs 3,000. Find the number of winners, if the total number of participants is 63.

Some more challenges...

1. Amina thinks of a number and subtracts 5 2 from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number?

2. A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?

3. Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?

4. One of the two digits of a two digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?

5. Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five years from now will be one third of his mother’s present age. What are their present ages?

6. There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4.At the rate Rs100 per metre it will cost the village panchayat Rs 75000 to fence the plot. What are the dimensions of the plot?

7. Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him Rs 50 per metre and trouser material that costs him Rs 90 per metre. For every 2 meters of the trouser material he buys 3 metres of the shirt material. He sells the materials at 12% and 10% profit respectively. His total sale is Rs 36,660. How much trouser material did he buy?

8. Half of a herd of deer are grazing in the field and three fourths of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.

9. A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages.

10. Aman’s age is three times his son’s age. Ten years ago he was five times his son’s age. Find their present ages.

SIMPLE EQUATION  for NIKUNJ and OM to be submitted 

2.1. Set up equations and solve them to find the unknown numbers in the following cases:

(a) Add 4 to eight times a number; you get 60.

(b) One fifth of a number minus 4 gives 3.

(c) If I take three fourths of a number and count up 3 more, I get 21.

 (d) When I subtracted 11 from twice a number, the result was 15.

(e) Munna subtracts thrice the number of notebooks he has from 50, he finds the result to be 8.

 (f) Ibenhal thinks of a number. If she adds 19 to it and divides the sum by 5, she will get 8.

(g) Anwar thinks of a number. If he takes away 7 from 5 2 of the number, the result is 11

 2 . 2. Solve the following:

(a) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. What is the lowest score?

(b) In an isosceles triangle, the base angles are equal. The vertex angle is 40°. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is 180°).

(c) Smita’s mother is 34 years old. Two years from now mother’s age will be 4 times Smita’s present age. What is Smita’s present age?

(d) Sachin scored twice as many runs as Rahul. Together, their runs fell two short of a double century. How many runs did each one score?

3. Solve the following:

 (i) Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. How many marbles does Parmit have?

(ii) Laxmi's father is 49 years old. He is 4 years older than three times Laxmi's age. What is Laxmi's age?

(iii) Maya, Madhura and Mohsina are friends studying in the same class. In a class test in geography, Maya got 16 out of 25. Madhura got 20. Their average score was 19. How much did Mohsina score?

(iv) People of Sundargram planted a total of 102 trees in the village garden. Some of the trees were fruit trees. The number of non-fruit trees were two more than three times the number of fruit trees. What was the number of fruit trees planted?

Arrange words and form meaningful sentences

Rearrange these words to make meaningful sentences.

1. ship violently the storm rocked the

2. masterpiece artist painstakingly the his worked at

3. gift free a Dad offered firm by the was.

4. I read paper in the burglar been caught had the that.

5. nightfall began cricketers the at their piercing calls.

6. wore a hat he of coconut made fiber his on head.

7. parts many coffee popular in world the is very of.

8. cave could explore not they torch the without a.

9. the storm shed damaged the was during.

10. the dog James talking sat next to himself to.

Answers

1. The storm rocked the ship violently.

2. The artist painstakingly worked at his masterpiece.

3. Dad was offered a free gift by the firm.

4. I read in the paper that the burglar had been caught.

5. The cricketers began their piercing calls at nightfall.

6. He wore a hat made of coconut fiber on his head.

7. Coffee is very popular in many parts of the world.

8. They could not explore the cave without a torch.

9. The shed was damaged during the storm.

10. James sat next to the dog talking to himself.

Sample 1: Diary writing

You are very excited as you are going for a school picnic with your classmates. Write a diary entry about your plan for the picnic. You are Ashok/Asin.

June 21, 2014

Saturday

11 PM

Dear Diary,

My class picnic

I am feeling very excited tonight. I am going on a picnic tomorrow with my classmates. Some of our teachers will also accompany us. We have been planning for this trip ever since our principal gave us permission a month ago. We are going to Nehru Park. It has a large ground where children can run around and play freely. I have packed some food items including potato chips and chewing gum. My mother has made a dozen sandwiches and a cake. My friends will also be bringing some food, and we shall all share and eat. I am also carrying my cricket bat with me. We plan to play a match.

I feel I just cannot go to sleep tonight. I keep imagining all the fun that we are going to have tomorrow. But my mother came into the room just now and warned me that if I do not go to sleep now, I might fall asleep at the picnic! As if that is ever going to happen! But maybe she’s right. So, good night!

Asin/Ashok

Sample 2:

You are Rohan studying in class VII. You went on a morning walk and saw a boy drowning in the water. You saved the boy. The crowd appreciated you. Write a diary entry for this incident.

The Top 10 Benefits of Watching Television:

1. Intelligence – Complex TV series such as Lost, Heroes and Battlestar Galactica require a great deal of thinking to understand what is happening. In fact, this was the argument of author Steve Johnson in his book Everything Bad is Good for You: How today’s popular culture is actually making us smarter. See also 8 TV Shows That Make You Smarter.

2. Learn about different people and places – While nothing beats actual travel for this type of learning, most people are limited in the amount of travel they can do. TV opens up the world, whether through watching documentaries, or drama series with multicultural characters.

3. Water Cooler effect – TV can often give office mates with little in common, something to talk about. This is especially so with series that lend themselves to discussion such as American Idol, Lost or major events such as the finale of The Sopranos.

4. Laughter – Laughing is good for us. As the saying goes, laughter is the best medicine. It has been found to increase circulation, lower blood pressure and more. Watching a good comedy on TV can be a great way to find something to laugh about.

5. How-To – With cable channels such as HGTV and the Food Network, you can learn how to do almost anything from your TV.

6. Excitement – Contest shows such as American Idol, Survivor and The Amazing Race give you the fun and excitement of having favorites and rooting for a winner. The benefits of sports for non-sports watchers.

7. Educational and Informative – With cable channels such as Discover, National Geographic and the History Channels, watching TV can be as educational as going to school. Plus, how many times have you learned something while watching a regular TV series? If it weren’t for all the police and lawyer shows on TV, would anybody other than lawyers know what Miranda rights were?

8. Memory – With all the serial shows on television, from the complex like Lost, to the soapy, like Grey’s Anatomy, we need to remember what has happened from week to week to enjoy them.

9. Makes exercise easier – When doing a stationary exercise like a treadmill, it can get very boring. Reading is difficult because of the movement. Music helps but doesn’t give you anything to look at. There must be a reason why there are televisions in most gyms.

10. Gives families something to bond over – my favorite reason. From the time that I watched Sesame Street and Mr. Rogers with my kids to the current day when we spend hours talking about Lost, Chuck, The Big Bang Theory, Heroes and The Office, television has led to some great conversations. Often, talking about something that occurred in a TV show will lead to discussions of real life situations. If that isn’t a benefit, I don’t know what is.

You cannot escape the responsibility of tomorrow by evading it today.

Abraham Lincoln

Introduction:

Generally the major persons of a country are called her citizens. The constitution of India has defined the qualifications to be an Indian citizen. Generally those who are born in India, who are born of the Indian parents and who are the long time residents of India are accepted as the Indian citizens. Besides, there are some special categories too. Every citizen has certain rights to enjoy. So he would have the obligation to do certain duties to his country an nation.

Rights and duties play an important part in the development of a nation or the growth of an organization. Rights on the one hand give an individual an opportunity to be a part of development process while duties on the other hand make an individual obliged to play a part in the development. As a citizen of a democratic country we all are privileged to have some fundamental rights. But, apart from these rights we also have fundamental duties which we rarely talk about. Moreover responsible citizenship is not just about enjoying the fundamental rights and performing the fundamental duties mentioned in our constitution but it is about going beyond those duties.

Rights:

The Constitution of India has granted some fundamental rights to her Citizens. there are seven in number, such as; (1) right to equality, (2) right to freedom, (3) right against exploitation, (4) right to freedom of religion, (5) cultural and education rights, (6) right to property and (7) right to constitutional remedies.

Right to equality: It guarantees equality of opportunity to all in public employments, without discrimination of religion, race, caste, sex or place of birth.

Right to freedom: It guarantees freedom of speech, peaceful assembly, formation of associations and unions, free movement in India, freedom of inhabitation anywhere in India, freedom of acquiring, holding and disposing of properties and freedom of practicing any trade or profession.

Right against exploitation: Forced labour and traffic in human beings are prohibited.

Right of freedom of religion: Freedom of religion is guaranteed subject to provisions for health, morality, peace and order.

Cultural and educational rights: Linguistic, cultural and religious interests of the minorities are protected. They an establish and administer their educational institutions.

Right to property: No person can be unlawfully deprived of this movable and immovable property.

Right to constitutional remedies: Any citizen can move the Supreme Court of India for the enforcement of his fundamental rights.

These rights are guaranteed by the Indian constitution. Any act of the Legislature which affects these fundamental rights can be challenged in a Court of Law.

Duties:

A citizen should have duties and responsibilities for his country. He should try to do the public good. He should control his conduct on the light of the good of his country. He should exercise his rights with proper judgment and obey the law of road and the like. He should try to build himself to do the best service for the country. He should have patriotism and fellow-feeling. As a citizen, he should know his responsibility to discharge his duties.

We always harp on our rights where ever we can and neglect the duties we generally have. As a citizen of our country we enjoy the rights of a privileged citizen and often we complain of the government's inability to provide services. Similarly in an organization, as an employee or a student in an institute we complain about the inadequacies of the system. But when it comes to our duty for the nation or institute, most of the times we are not aware at all. For instance as a responsible citizen, we have the duty of protecting the public properties, which we do not hesitate to destroy while protesting or demanding our rights. Destroying street lamps, burning tyres and vehicles, disrupting traffic are the common phenomena seen at the protest sites. Do we really need to do this? Have we ever realized the losses we cause to our country or organization in this manner? Do we ponder for a moment, how much effort it takes to build those structures?

Conclusion:

It is a matter of regret that most of the Indian citizens are neglectful of their duties to India. However, it is hoped, our student community will do their duties to the country, while enjoying the rights, guaranteed by the Constitution.

We the  People, recognize that we have responsibilities as well as rights; that our destinies are bound together; that a freedom which only asks what's in it for me, a freedom without a commitment to others, a freedom without love or charity or duty or patriotism, is unworthy of our founding ideals, and those who died in their defence. We are empowered by the constitution where we have been given the rights are given but the same constitution is also having the duties of a citizen which however is ignored  by our generation.

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