__Examples__1. If 2x+3y=34 and ((x + y)/y)=13/8,then find the value of 5y+7x.

2. If 2x+3y+z=55,x-y=4 and y – x + z=12,then what are the values of x , y and z?

3. Find the value of (1-(1/3))(1-(1/4))(1-(1/5))….(1-(1/100)).

4. Find the value of (1/(2*3))+(1/(3*4))+(1/(4*5))+(1/(5*6))+…..+ ((1/(9*10)).

5. A board 7ft. 9 inches long is divided into 3 equal parts. What is the length of each part?

6. A man divides Rs. Among 5 sons,4 daughters and 2 nephews .If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews ,how much does each daughter receive?

7. A man spends 2/5 of his salary on house rent, 3/10 of his salary on food and 1/8 of his salary on conveyance. If he has Rs.1400 left with him, find his expenditure on food and conveyance.

8. A third of Arun’s marks in mathematics exceeds a half of his marks in English by 80.if he got 240 marks In two subjects together how many marks did he got in English?

9. A tin of oil was 4/5full.when 6 bottles of oil were taken out and four bottles of oil were poured into it, it was ¾ full. How many bottles of oil can the tin contain?

10. If 1/8 of a pencil is black ½ of the remaining is white and the remaining 3 ½ is blue find the total length of the pencil?

11. In a certain office 1/3 of the workers are women ½ of the women are married and 1/3 of the married women have children if ¾ of the men are married and 2/3 of the married men have children what part of workers are without children?

12. A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsalable and there are 12 unsalable mangoes in the crate then how many mango are there in the crate?

13. A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280more at the second station it drops one half the new total and takes twelve more .on arriving at the third station it is found to have 248 passengers. Find the no of passengers in the beginning?

14. If a

^{2}+b^{2}=177and ab=54 then find the value of a+b/a-b?15. Village X has a population of 68000,which is decreasing at the rate of 1200 per year.VillagyY has a population of 42000,which is increasing at the rate of 800 per year .in how many years will the population of the two villages be equal?

16. From a group of boys and girls,15 girls leave. There are then left 2 boys for each girl. After this, 45 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning?

17. An employer pays Rs.20 for each day a worker works and forfeits Rs.3 for each day is ideal at the end of sixty days a worker gets Rs.280. For how many days did the worker remain ideal?

18. kiran had 85 currency notes in all , some of which were of Rs.100 denomination and the remaining of Rs.50 denomination the total amount of all these currency note was Rs.5000.how much amount did she have in the denomination of Rs.50?

19. When an amount was distributed among 14 boys, each of them got rs 80 more than the amount received by each boy when the same amount is distributed equally among 18 boys. What was the amount?

20. Mr. Bhaskar is on tour and he has Rs. 360 for his expenses. If he exceeds his tour by 4 days, he must cut down his daily expenses by Rs. 3. for how many days is Mr. Bhaskar on tour?

21. Two pens and three pencils cost Rs 86. four Pens and a pencil cost Rs. 112. find the cost of a pen and that of a pencil.

22. Arjun and Sajal are friends. Each has some money. If Arun gives Rs. 30 to Sajal, the Sajal will have twice the money left with Arjun. But, if Sajal gives Rs. 10 to Arjun, the Arjun will have thrice as much as is left with Sajal. How much money does each have?

23. In a caravan, in addition to 50 hens there are 45 goats and 8 camels with some keepers. If the total number of feet be 224 more than the number of heads, find the number of keepers.

__Exercise__1. Income of a company doubles after every one year. If the initial income was Rs. 4 lakhs, what would be the income after 5 years?

2. On sports day, if 30 children were made to stand in a column, then 16 columns could be formed. If 24 children were made to stand in a column, then how many columns could be formed?

3. The number of students in each section of a school is 24. After admitting new students, three new sections were started. Now, the total number of sections is 16 and there are 21 students in each section. The number of new students admitted is:

4. A class starts at 10 a.m. and lasts till 1.27 p.m. Four periods are held during this interval. After every period, 5 minutes are given free to the students. The exact duration of each period is:

5. A light was seen at intervals of 13 seconds. It was seen for the first time at 1 hr. 54 min 50 secs. a.m. and the last time at 3 hrs. 17 min. 49 secs. a.m. How many times was the light seen?

6. Along a yard 225 metres long, 26 trees are planted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees?

7. A man earns Rs. 20 on the first day and spends Rs. 15 on the next day. He again earns Rs. 20 on the third day and spends Rs. 15 on the fourth day. If he continues to save like this, how soon will he have Rs. 60 in hand?

8. It costs Rs. x each to make the first thousand copies of a compact disc and Rs. y to make each subsequent copy. If z is greater than 1000, how much will it cost to make z copies of the compact disc?

9. A boy was asked to multiply a number by 25. He instead multiplied the number by 52 and got the answer 324 more than the correct answer. The number to be multiplied was :

10. David got two and a half times as many marks in English as in History. If his total marks in the two subjects are 140, the marks obtained by him in English are :

11. The total monthly salary of 4 men and 2 women is Rs. 46,000. If a woman earns Rs. 500 more than a man, what is the monthly salary of a woman?

12. Water boils at 212

^{o}F or 100^{o}C and melts at 32^{o}F or 0^{o}C. If the temperature of a particular day is 35^{o}C, it is equivalent to :13. The number of girls in a class is 5 times the number of boys. Which of the following cannot be the total number of children in the class?

14. A boy multiplied 423 by a number and obtained 65589 as his answer. If both the fives in the answer are wrong and all other figures are correct, the correct answer is :

15. A pineapple costs Rs. 7 each. A watermelon costs Rs. 5 each. X spends Rs. 38 on these fruits. The number of pineapples purchased is.:

16. A sum of Rs. 750 is distributed among A, B, C and D in such a manner that A gets as much, as B and C together, B gets Rs. 125 more than C and D gets as much as C. What is A’s share?

17. The total number of digits used in numbering the pages of a book having 366 pages, is :

18. A bonus of Rs. 1000 is to be divided among three people so that Rohit receives twice as much as Sachin, who receives one-fifth as much as Gagan. How much money should Gagan receive?

19. A printer numbers the pages of a book starting with 1 and uses 3189 digits in all. How many pages does the book have?

20. In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is :

21. What fraction of an hour is a second?

22. When a ball bounces, it rises to ¾ of the height from which it fell. If the ball is dropped from a height of 32 m, how high will it rise at the third bounce?

23. Sanket earns twice as much in the month of March as in each of the other months of the year. What part of his entire annual earnings was earned in March?

24. A person travels 3.5 km from place A to place B. Out of this distance, he travels 1 2/3 km on bicycle, 1 1/6 km on scooter and the rest on foot. What portion of the whole distance does he cover on foot?

25. If one-third of a tank holds 80 litres of water, then the quantity of water that half of the tank holds is :

26. A certain amount is distributed among A, B and C. A gets 3/16 and B gets ¼ of the whole amount. If C gets Rs. 81, then B gets :

27. A student was asked to find the value of 3/8 of a sum of money. The student made a mistake by dividing the sum by 3/8 and thus got an answer which exceeded the correct answer by Rs. 55. The correct answer was :

28. In an examination, a student was asked to find 3/14 of a certain number. By mistake, he found ¾ of that number. His answer was 150 more than the correct answer. The number is :

29. A sum of Rs. 1360 has been divided among A, B and C such that A gets 2/3 of what B gets and B gets ¼ of what C gets. B’s share is :

30. In a family, the father took ¼ of the cake and he had 3 times as much as each of the other members had. The total number of family members is :

31. N number of persons decided to raise Rs. 3 lakhs by equal contributions from each. Had they contributed Rs. 50 each extra, the contribution would have been Rs. 3.25 lakhs. How many persons are there?

32. Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed?

33. David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross?

34. A classroom has equal number of boys and girls. Eight girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially?

35. After distributing the sweets equally among 25 children, 8 sweets remain. Had the number of children been 28, 22 sweets would have been left after equally distributing. What was the total number of sweets?

36. In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for?

37. Each boy contributed rupees equal to the number of girls and each girl contributed rupees equal to the number of boys in a class of 60 students. If the total contribution thus collected is Rs. 1600, how many boys are there in the class?

38. A sum of Rs. 312 was divided among 100 boys and girls in such a way that each boy gets Rs. 3.60 and each girl Rs. 2.40. The number of girls is :

39. A worker may claim Rs. 1.50 for each km which he travels by train and 50 p for each km he drives his own car. If in one week he claimed Rs. 50 for travelling 80 km, how many kms did he travel by train?

40. In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts in all 60 questions and secures 130 marks, the number of questions he attempts correctly, is :

41. A cricket team won 3 matches more than they lost. If a win gives them 2 points and loss (- 1) point, how many matches, in all, have they played if their score is 23?

42. A total of 324 coins of 20 paise and 25 paise make a sum of Rs. 71. The number of 25-paise coins is :

43. On Children’s Day, sweets were to be equally distributed among 175 children in a school. Actually on the Children’s Day, 35 children were absent and therefore each child got 4 sweets extra. Total how many sweets were available for distribution?

44. A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?

45. A number of friends decided to go on a picnic and planned to spend Rs. 96 on eatables. Four of them, however, did not turn up. As a consequence, the remaining ones had to contribute Rs. 4 each extra. The number of those who attended the picnic was :

46. Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by :

47. A certain number of tennis balls were purchased for Rs. 450. Five more balls could have been purchased in the same amount if each ball was cheaper by Rs. 15. The number of balls purchased was :

48. A piece of cloth costs Rs. 35. If the length of the piece would have been 4 m longer and each metre costs Re. 1 less, the cost would have remained unchanged. How long is the piece?

49. In a certain shop, 9 oranges cost as much as 5 apples, 5 apples cost as much as 3 mangoes and 4 mangoes cost as much as 9 lemons. If 3 lemons cost Rs. 4.80, the price of an orange is :

50. If 2 tables and 3 chairs cost Rs. 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost? The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay?

51. The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is :

52. The taxi charges in a city comprise of a fixed charge, together with the charge of the distance covered. For a journey of 16 km, the charges paid are Rs. 156 and for a journey of 24 km, the charges paid are Rs. 204. What will a person have to pay for travelling a distance of 30 km?

53. In a classroom, if 6 students per bench are assigned to accommodate all students, one more bench will be required. However, if 7 students are accommodated per bench, there would be a space left for 5 students. What is the number of students in the class?

54. There are two examination rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is :

55. In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group?

56. Vidushi and Sanya distribute Rs. 100 each in charity. Vidushi distributes money to 5 more people than Sanya and Sanya gives each Re. 1 more than Vidushi. How many people are recipients of the charity?