We provide linear equations in two variables practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on linear equations in two variables skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of linear equations in two variables Questions

Question No | Questions | Class |
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1 | The denominator of a fraction is greater than its numerator by ( 7 . ) If 4 is added to both its numerator and denominator, then it becomes ( frac{1}{2} . ) Find the fraction. A ( cdot frac{1}{6} ) B. ( frac{7}{3} ) ( c cdot frac{3}{10} ) D. 6 ( overline{7} ) | 9 |

2 | 65. If the sum of the two num- bers is 120 and their quotient is 5, then the difference of the two numbers is : (1) 115 (2) 100 (3) 80 (4) 72 | 9 |

3 | 65. If a train runs at 40 km/hr, it reaches its destination late by 11 minutes, but if it runs at 50 km/hr, it is late by 5 minutes only. Find, the correct time for the train to complete its jour- ney. (1) 19 minutes (2) 20 minutes (3) 21 minutes (4) 18 minutes | 9 |

4 | Simplify: ( (2 x+y)^{3}+(2 x-y)^{3} ) | 9 |

5 | The cost of 2 kg of Apples and 1 kg grapes on a day was bound to be Rs. 160 After a moth the lost of 4 kg grapes and 2 kg graps is Rs. 300. Represent this situation algebraicallyand geometrically. | 9 |

6 | If point (3,0) lies on the graph of the equation ( 2 x+b y=k, ) then the value of ( k^{prime} ) is : ( mathbf{A} cdot mathbf{6} ) B. 3 ( c cdot 2 ) D. | 9 |

7 | 58. If x + y = 318. x-y= 12. then the value of xy (x2 + y) is (1) 5760 (2) 5440 (3) 5360 (4) 5180 | 9 |

8 | f ( 2 x-3 y=-8 ) and ( 4 x+3 y=2 ) then find the value of ( x ) | 9 |

9 | Write any one linear equation using the variables ‘ ( x ) ‘ and ‘ ( y ) ‘. | 9 |

10 | ( mathbf{0 . 2 x + 0 . 1 y}=mathbf{2 5} ) ( mathbf{2 ( x – 2 ) – 1 . 6 y}=mathbf{1 1 6} ) | 9 |

11 | 1 10. One number is three times another. If the larger number is subtracted from 60, the result is 5 less than the smaller number subtracted from 55. Find the numbers. | 9 |

12 | What are the two numbers whose sum is 58 and difference is ( 28 ? ) | 9 |

13 | 52. The sum of the numerator and denominator of a positive fraction is 11. If 2 is added to both nu- merator and denominator, the fraction is increased by 24 The difference of numerator and de- nominator of the fraction is (1) 5 (2)3 (3) 1 (4) 9 | 9 |

14 | A train 110 metres long is running with a speed of ( 60 mathrm{km} / mathrm{hr} ). In what time it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? A . 5 sec B. 6 sec ( c cdot 7 sec ) D. 10 sec | 9 |

15 | 59. An equation of the form ax + by + c = 0 where a 0, b 0 , C=0 represents a straight line which passes through (1) (0, 0) (2) (3, 2) (3) (2, 4) (4) None of these | 9 |

16 | Factorize the following using appropriate identities: ( (mathrm{i}) 9 x^{2}+6 x y+y^{2} ) ( (mathrm{ii}) 4 boldsymbol{y}^{2}-mathbf{4} boldsymbol{y}+mathbf{1} ) ( (i i i) x^{2}-frac{y^{2}}{100} ) | 9 |

17 | 60. The ratio between two numbers is 2 : 3. If each number is in- creased by 4, the ratio between them becomes 5:7. The differ- ence between the numbers is (1) 8 (2) 6 (3) 4 (4) 2 | 9 |

18 | The sum of the digits of a two-digit number is ( 12 . ) The number obtained by interchanging the two digits exceeds the given number by ( 18 . ) Find the number. A . 57 B. 42 ( c cdot 69 ) D. 84 | 9 |

19 | What is the value of a for which the system of linear equations ( a x+3 y=a ) ( 3 ; 12 x+a y=a ) has no solution ( mathbf{A} cdot a=6 ) B . ( a=-3 ) ( mathbf{c} cdot a=3 ) D. ( a=-6 ) | 9 |

20 | 2 tables and 3 chairs cost Rs.2000 Where as 3 tables and 2 chairs cost Rs. 2500.Find the total cost of 1 table and 5 chairs. | 9 |

21 | Two pipes running together can fill a cistern in ( 3 frac{1}{13} ) minutes. If one pipe takes 3 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern. | 9 |

22 | Find the value of ( k ) for which the following system of equations has no solution: ( boldsymbol{x}+mathbf{2} boldsymbol{y}=mathbf{0} ) ( 2 x+k y=5 ) | 9 |

23 | Find the value of ( k ) for which the following system of equations has no solution: ( mathbf{2} boldsymbol{x}+boldsymbol{k} boldsymbol{y}=mathbf{1 1} ) ( 5 x-7 y=5 ) | 9 |

24 | The present age of a man is twice that of his son.After Eight years their ages will be in the ratio 7: 4 . Find the son’s present age. A. 24years B. 34years c. 44years D. 54years | 9 |

25 | buy 40 animals consisting of rams at 4 pounds, pigs at 2 pounds, and oxen at 17 pounds. if I spend 301 pounds, how many of each do I buy? | 9 |

26 | ff ( x=2 k+1 ) and ( y=k ) is a solution of the equation ( 5 x+3 y-7=0, ) find the value of ( k ) | 9 |

27 | Solve ( 9 x-4 y=8 & 13 x+7 y=10 ) A. ( x=7, y=3 ) в. ( x=9, y=3 ) c. ( x=1, y=3 ) D. ( x=4, y=7 ) | 9 |

28 | State true or false: The graph of the linear equation ( x+ ) ( 2 y=7 ) passes through the point (0,7) A . True B. False | 9 |

29 | CM. If 12. area of e givne (c) 45 The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is Then the rational number is angle | 9 |

30 | Mothers present age is 6 times the age of her son, After 5 years the mothers age will be 4 times that times the age of her son. What will be the presents age of a son? | 9 |

31 | If ( x=a, y=b ) is the solution of the equations ( x-y=2 ) and ( x+y=4 ) then the value of a and b are respectively A . 1 and 3 B. 3 and 2 ( c .3 ) and 1 D. -1 and -3 | 9 |

32 | Scooter charges consist of fixed charges and remaining depend kilometers. If a person travels ( 12 mathrm{km}, ) he pays Rs.45 and for tra Express the above statements in the from of simultaneous equation and find charges of rate per ( mathbf{k m} ) | 9 |

33 | Simplify ( left(2 x+frac{1}{3 y}right)^{2}-left(2 x-frac{1}{3 y}right)^{2} ) A ( cdot frac{4 x}{3 y} ) в. ( 2left(4 x^{2}+frac{1}{9 y^{2}}right) ) c. ( frac{8 x}{3 y} ) D. ( frac{4 y}{3 x} ) | 9 |

34 | UJNI Two numbers are in the ratio 5: 3. If they differ by 18, then. The numbers are (a) 45,27 (b) 25, 15 (c) 35,21 (d) 65,39 | 9 |

35 | The pair of equations ( boldsymbol{x}=boldsymbol{a} ) and ( boldsymbol{y}=boldsymbol{b} ) graphically represents lines which are A. parallel B. intersecting at ( (b, a) ) c. coincident D. intersecting at ( (a, b) ) | 9 |

36 | 10. Anima left one-half of her property to her daughter, one- third to her son and donated the rest to an educational institute. If the donation was worth 1,00,000, how much money did Anima have? the month of February in | 9 |

37 | Intersecting point of ( boldsymbol{x}+boldsymbol{y}=boldsymbol{6}, boldsymbol{x}- ) ( boldsymbol{y}=boldsymbol{4} ) is | 9 |

38 | Find two solutions for each of the following equations: ( mathbf{2} boldsymbol{x}+mathbf{3} boldsymbol{y}+mathbf{7}=mathbf{0} ) | 9 |

39 | For all real numbers ( b ) and ( c ) such that the product of ( c ) and 3 is ( b ), the expression which represents the sum of ( c ) and 3 in terms of ( b ) is B. ( 3 b+3 ) ( c cdot 3(b+3) ) D. ( frac{b+3}{3} ) E ( cdot frac{b}{3}+3 ) | 9 |

40 | Write a linear equation in two variables to represent the following statement Two numbers are such that 2 times of one is same as 3 times of the other. A. ( 2 x=3 y, ) where ( x= ) first number and ( y=operatorname{second} ) number B. ( 2 x=-3 y ), where ( x= ) first number and ( y=operatorname{second} ) number c. ( 2 x=7 y ), where ( x= ) first number and ( y=operatorname{second} ) number D. ( x=3 y ), where ( x= ) first number and ( y=operatorname{second} ) number | 9 |

41 | Duul II=I+11 = 12 cm A number consists of two digits. The digit at ten’s place is two times the digit at the reversing the digits, is 27 less than the original number. Find the original number. atten’s place is two times the digit at the unit’s place. The number formed by Sol. Let the digit at units place = x | 9 |

42 | 5 pencils and 7 pens together cost Rs. ( mathbf{5 0}, ) whereas ( mathbf{7} ) pencils and ( mathbf{5} ) pens together cost Rs. ( 46 . ) The cost of one pencil is A. Rs. в. Rs. c. Rs. D. Rs. | 9 |

43 | 9. u pa ulicascoy 0. wo equal sides of a triangle are each 4m less than three times the third side. Find the dimensions of the triangle, 11 its perimeter is 55m. her daughter, one- | 9 |

44 | 11. Deveshi has a total of 590 as currency notes in the denominations of 50, 20 and 10. The ratio of the number of 50 notes and 20 notes is 3:5. If she has a total of 25 notes, how many notes of each denomination she has? D . | 9 |

45 | A machine takes 2 litres of petrol to start and then 3 litres per hour while running. What will the no. of hours for which machine run if total 20 litres of petrol is used? A .4 B. 5 ( c cdot 6 ) D. 8 | 9 |

46 | Write one solution of the equation ( 2 x+ ) ( boldsymbol{y}=mathbf{1 0} ) | 9 |

47 | 11. Raju and his grandfather have an age difference of 65 years at present. After 10 years the sum of their age is 95 years. What is the present age of Raju and his grandfather? (1) 15 & 80 (2) 10 & 65 (3) 5 & 70 (4)5 & 65 | 9 |

48 | Ten students of class ( X ) took part in Mathematics quiz. If the number of girls is 4 more than the number of boys. Represent this situation algebraically. | 9 |

49 | ( y=2 x+3 ) intersecting lines | 9 |

50 | Illustration 2.10 Plot the line 2x – 3y = 12. | 9 |

51 | The condition that the equation ( a x+ ) ( b y+c=0 ) represent a linear equation in two variables is : A ( . a neq 0, b=0 ) в. ( b neq 0, a=0 ) c. ( a=0, b=0 ) D. ( a neq 0, b neq 0 ) | 9 |

52 | A fraction becomes ( frac{1}{3} ) when 1 is subtracted from the numerators and it becomes ( frac{1}{4} ) when 8 is added to its denominator. Find the fraction. | 9 |

53 | 9. 1 300 is divided into two parts such that half of one part is less than the other by 48. Find the two parts. | 9 |

54 | Write four solutions for the following equation. ( x=4 y ) ( A ldots(0,1),(4,1) ;(8,2) ) and (12,3) ( B ldots(0,0),(4,2) ;(8,2) ) and (12,3) ( (-infty, 0),(4,1) ;(8,3) ) and (12,3) ( D ldots(0,0),(4,1) ;(8,2) ) and (12,3) | 9 |

55 | Advanced purchase tickets to an art exhibition cost 34, while tickets purchased at the door cost *6. If a total of 150 tickets were sold and 1680 was collected, how many advanced purchase tickets were sold? | 9 |

56 | Father’s age is 10 more than twice age of his son. What is the number of variables if the statement is written in the form of linear equation? A. one B. Two c. Multivariable D. Non-linear | 9 |

57 | If ( f(x)=frac{2}{3} x+7, ) find the value of ( f(x) ) if ( boldsymbol{x}=mathbf{3} ) A. – – B . – – ( c cdot 6 ) D. | 9 |

58 | Express the following statements as a linear equation in two variable. The cost of a ball pen is Rs. 5 less than half the cost of a fountain pen. | 9 |

59 | Find three different solution of the equation ( 3 x=7 y-21 ) | 9 |

60 | The two numbers whose surn is 28 and difference is 4 are 18 and 10. | 9 |

61 | ( operatorname{lt} frac{x}{a}+frac{y}{b}=a^{2}+b^{2} ) and ( frac{x}{a^{2}}+frac{y}{b^{2}}=a+ ) ( boldsymbol{b} ) then ( boldsymbol{x}=? ) ( mathbf{A} cdot a ) B ( cdot a^{2} ) ( c cdot a^{3} ) D. ( a^{4} ) | 9 |

62 | The sum of ( frac{1}{x+y} ) and ( frac{1}{x-y} ) is A ( cdot frac{2 y}{x^{2}-y^{2}} ) в. ( frac{2 x}{x^{2}-y^{2}} ) c. ( frac{2 x}{y^{2}-x^{2}} ) D. ( -frac{2 y}{x^{2}-y^{2}} ) | 9 |

63 | Write constant term ( x^{2} y+x y^{2}+5 x y-4 ) | 9 |

64 | The difference of two numbers is 3 and the difference of their square is ( 69 . ) Find the numbers. A. 3 and 9 B. 13 and 10 c. 11 and 18 D. 5 and 2 | 9 |

65 | Solve ( 2 x+3=5 x+6 & ) represent it as ¡) One variable ii) Two variable | 9 |

66 | 59. If x : y = 4:5, then (3x + y) : (5x + 3y) = (1) 3:5 (2) 5:3 (3) 17:35 (4) 35 : 17 | 9 |

67 | 11. A man was engaged as typist for the month of February in 2009. He was paid 500 per day but 100 per day were deducted for the days he remained absent. He received 59,100 as salary for the month. For how many days did he work? | 9 |

68 | 69. If a, b are rational numbers and (a – 1)/2 +3 = b 2 +a, the value of (a + b) is (1)-5 (2)3 (3)-3 (4)5 | 9 |

69 | Find the value of ( boldsymbol{m}, ) if ( boldsymbol{x}=boldsymbol{2}, boldsymbol{y}=mathbf{1} ) is a solution of the equation ( 2 x+3 y=m ) | 9 |

70 | Find the least values of ( x ) and ( y ) which satisfy the equations: ( 77 y-30 x=295 ) A . ( x=32, y=27 ) в. ( x=21, y=34 ) c. ( x=47, y=35 ) D. ( x=46, y=32 ) | 9 |

71 | Write any one solution of equation ( boldsymbol{x}+ ) ( 2 y=7 ) | 9 |

72 | ( frac{2 x}{3}-frac{x-1}{6}+frac{7 x-1}{4}=2 frac{1}{6} ) Hence, find the value of ( x ) and ( a ), if ( frac{1}{a}+ ) ( mathbf{5} boldsymbol{x}=mathbf{8} ) A ( x=2 ) and ( a=frac{1}{2} ) B. ( x=3 ) and ( a=frac{1}{4} ) c. ( _{x}=4 ) and ( a=frac{1}{5} ) D. ( x=1 ) and ( a=frac{1}{3} ) | 9 |

73 | Rakesh went to a stationary shop to purchase a total of 38 pens, erasers and sharpeners. He purchased at least 11 items of each. He purchased more sharpeners than erasers and more erasers than pens. If each pen cost Rs. 2 each eraser cost Rs. 3 and each sharpener cost Rs. ( 4 . ) find the minimum expenditure be could have incurred on the items (in Rs.) A . 116 B . 118 c. 117 D. 119 | 9 |

74 | Solve ( mathbf{2} boldsymbol{x}-boldsymbol{y}=mathbf{6}, boldsymbol{x}-boldsymbol{y}=mathbf{2} ) | 9 |

75 | Solve the following systems of equations: ( frac{1}{2 x}+frac{1}{3 y}=2 ) ( frac{1}{3 x}+frac{1}{2 y}=frac{13}{6} ) | 9 |

76 | The equation ( 2 x-5 y=9 ) has: A. no solution B. one solution c. two solutions D. infinitely many solutions | 9 |

77 | Check if ( left(frac{1}{2}, 2right) ) is a solution of ( 2 x-5 y= ) 10 | 9 |

78 | 12 6. The sum of three numbers is 98. The ratio of the first to the second is = and the ratio of the second to the third is – 3 the Find the second number. 13. | 9 |

79 | A boat whose speed in ( 15 k m / h r ) in still water goes ( 30 mathrm{km} ) downstream and comes back in a total of 4 hours 30 minutes. the speed of the stream (in ( mathrm{km} / mathrm{hr}) ) is : | 9 |

80 | f ( 2 y-x=8, ) and ( 3 x-y=1, ) what is the value of ( x ? ) A B. 2 ( c cdot 3 ) D. – | 9 |

81 | Obtain pair of linear equations in two variables: In a cricket match, rohit makes his score twice Dhawan’s scored Both of them together make a total score 150 runs. | 9 |

82 | 67. If 999x + 888y = 1332 and 888x + 999y = 555, then x2y2 is equal to (1) 9 (2) 5 (3) 7 (4) 8 | 9 |

83 | For some data ( M+bar{X}=22 ) and ( M- ) ( bar{X}=2, ) then ( Z=dots ) A . 14 B . 15 c. 16 D. 12 | 9 |

84 | f ( x=b-c, y=c-a, z=a-b ) then the value of ( x^{2}-y^{2}+z^{2}+2 x z ) is ( A cdot 2 ) B. – ( c cdot 0 ) D. | 9 |

85 | The units digit of a two-digit number is greater than its tens digit by 2 and the product of that number by the sum of its digits is ( 144 . ) Find the number. | 9 |

86 | Solve the system ( : mathbf{6} boldsymbol{x}+mathbf{5} boldsymbol{y}=-mathbf{3}, boldsymbol{y}= ) ( -2 x-7 ) A. (-2,4) () в. (-1,2) c ( .(-8,9) ) D. (-7,8) | 9 |

87 | In the given equation ( a=frac{2}{3} b+5 . ) If ( b=6, ) then ( a=? ) ( A cdot 7 ) B. 9 c. 11 D. 13 | 9 |

88 | Denominator of a Fraction exceeds its numeration by ( 6 . ) If 1 is added to the numerator and 3 is substracted from the denominater, the new friction is ( frac{3}{4} . ) find the orignal fraction | 9 |

89 | Solve the given pair of linear equations: ( frac{3}{sqrt{x}}+frac{4}{sqrt{y}}=2, frac{5}{sqrt{x}}+frac{7}{sqrt{y}}= ) ( frac{41}{12}(x>0, y>0) ) | 9 |

90 | Solve the following systems of equations: ( frac{1}{5 x}+frac{1}{6 y}=12 ) ( frac{1}{3 x}-frac{3}{7 y}=8, x neq 0, y neq 0 ) | 9 |

91 | 16. Hasan buys nvo kinds of cloth materials for school uniforms, shirt material that costs him 50 per metre and trouser material that costs him 90 per metre. For every 3 metres of the shirt material, he buys 2 metres of the trouser material He sells the materials at 12% and 10% profit respectively His total sale is R36,600. How much trouser material did he buy? | 9 |

92 | 52. The sum of two numbers is 75 and their difference is 25. The product of the two numbers is : (1) 1350 (2) 1250 (3) 125 (4) 1000 | 9 |

93 | The number of integral values of ( boldsymbol{m}, ) for which the ( x ) -coordinate of the point of intersection of the lines ( 3 x+4 y=9 ) and ( y=m x+1 ) is also an integer is A .2 B. ( c cdot 4 ) D. | 9 |

94 | If ( 2 x-y=4 ) and ( x+y=5, ) then the value of ( x y ) is A . 4 B. 6 c. 8 D. | 9 |

95 | 7. The difference between two natural numbers is 96. If the larger number is divided by the smaller one, then the quotient is 6 and the remainder is 11. Find the numbers. | 9 |

96 | (u 100,200,190 S 11. Sum of the digits of a two digit number is 9. When we interchange the digits, it is found that the resulting two digit new number is greater than the original number by 27. Then the two digit number is (a) 63 (b) 36 (c) 45 (d) 54 | 9 |

97 | In the following given systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it ( 2 x+y=5 ) ( 4 x+2 y=10 ) | 9 |

98 | Write any four solution of the equation ( boldsymbol{x}+boldsymbol{y}=mathbf{2} ) | 9 |

99 | Write the following equation in the general form of a linear equation in two variables: ( 7 x=3 y+23 ) | 9 |

100 | f ( x+y=3 ) and ( 3 x-2 y-4=0 ) find ( boldsymbol{x}, boldsymbol{y} ) | 9 |

101 | 12x +1 The equation – pr 13x-1 – + 3 is true for 3. The equation 12x+1 – 13x=1+3 is true for (b) x=2 | 9 |

102 | Express the given statements in the form linear equations in two variables. One is added to numerator and 4 is subtracted from denominator, the fraction becomes 1. | 9 |

103 | An auto charges Rs. 15 for first kilometer and Rs. 8 each for each subsequent kilometer. For a total distance of ( ^{prime} x^{prime} k m ) an amount of Rs. ( ^{prime} y^{prime} ) is said. Write the linear equation representing this information | 9 |

104 | Find the value of ( k ) for which each of the following systems of equations have infinitely many solution: ( boldsymbol{x}+(boldsymbol{k}+mathbf{1}) boldsymbol{y}=boldsymbol{4} ) ( (k+1) x+9 y=5 k+2 ) | 9 |

105 | A part of the monthly expenses of a family is constant and the remaining varies with the price of wheat. When the price of wheat is Rs. 250 per quintal, the total monthly expenses are Rs. 1000 and when it is Rs. 240 per quintal, the total monthly expenses are Rs. 980 per quintal. The total monthly expenses of the family when the cost of wheat is Rs. 350 per quintal, will be: A . Rs. 500 B. Rs. 1200 c. Rs. -1200 D. Rs. – 500 | 9 |

106 | Solve the following pair of simultaneous equations: ( frac{boldsymbol{x}}{mathbf{3}}+boldsymbol{y}=mathbf{1 . 7} ) and ( frac{mathbf{1 1}}{boldsymbol{x}+underline{boldsymbol{y}}}=mathbf{1 0} ) for all ( left[boldsymbol{x}+frac{boldsymbol{y}}{mathbf{3}} neq mathbf{0}right] ) A ( . x=2 ) and ( y=7 ) В. ( x=0.9 ) and ( y=-2.5 ) c. ( x=0 ) and ( y=-4 ) D. ( x=0.6 ) and ( y=1.5 ) | 9 |

107 | The ages of two persons differ by 16 years. If 6 years ago, the elder one be 3 times as old as the younger one, find their present ages. A. 15 years and 31 years B. 14 years and 30 years c. 12 years and 28 years D. 10 years and 26 years | 9 |

108 | The difference of two numbers is 5 and the difference of their reciprocals is ( frac{1}{10} ) Find the numbers. A. 10,50 в. 10,5 c. 10,-510,-5 D. 0,5 | 9 |

109 | Consider the equation: ( boldsymbol{y}+mathbf{7} boldsymbol{x}=mathbf{3} boldsymbol{x}-mathbf{2} boldsymbol{y}+mathbf{2 8} ) f ( boldsymbol{y}=mathbf{2}, ) what is the value of ( boldsymbol{x} ) ? ( mathbf{A} cdot mathbf{5} ) B. 5.5 ( c cdot 6 ) D. 6.5 | 9 |

110 | 57. If 2r = h + Vr2 +h2, (r + 0), then find r: h. (1) 1 : 2 (2) 3:1 (3) 1:1 (4) 4:3 | 9 |

111 | Two men and 7 children complete a certain piece of work in 4 days while 4 men and 4 children complete the same work in only 3 days. The number of days required by 1 man to complete the work is A. 60 days B. 15 days c. 6 days D. 51 days | 9 |

112 | Five years ago, Shikha was thrice as old as Rani. 10 years later, Shikha will be twice as old as Rani. How old are they now? A. Rani 20 yrs, Shikha 50 yrs B. Shikha 20 yrs, Rani 50 yrs c. Shikha 80 yrs, Rani 30 yrs D. Shikha 30 yrs, Rani 80 yrs | 9 |

113 | 14 The organisers of an essay competition decide that a winner in the competition gets a prize of 100 and a participant who does not win gets a prize of 25. The total prize money distributed is *3.000. Find the number of winners if the total number of participants is 03 | 9 |

114 | Check if (0,-2) is a solution of ( 2 x-5 y= ) 10 | 9 |

115 | 9. The ages of Rahul and Haroon are in the ratio 5 : 7. If four years later, the sum of their ages will be 56 years, then Rahul’s present age is (a) 28 years (b) 26 years (c) 20 years (d) 18 years A hen cantoins 50P 25P and 10P coins in the ratio 2.3.4. | 9 |

116 | Find the value of ( k, ) if ( x=2, y=1 ) is a solution of the equation ( 2 x+3 y=k . ) Find two more solutions of the resultant equation. | 9 |

117 | Find out which of the following equations have ( x=2, y=1 ) as a solution: ( 2 x+3 y=1 ) | 9 |

118 | The average of six number is 12 and The average of 4 numbers is 15 what is the average of these 10 number? | 9 |

119 | If ( c ) is 6 less than thrice of ( b ), which of the following represents the relation between b and c? A ( cdot c=frac{b-2}{3} ) B. ( c=frac{b+2}{3} ) c. ( c=3 b-2 ) ( mathbf{D} cdot c=3 b-6 ) | 9 |

120 | Find three different solution of the each of the equation. ( 3 x+4 y=7 ) | 9 |

121 | If ( frac{7}{2} x+frac{5}{2} y=5 ; 4 x+2 y=7, ) then what is the value of ( boldsymbol{x}-boldsymbol{y} ? ) ( mathbf{A} cdot mathbf{1} ) B. 4 c. 2 D. – | 9 |

122 | 54. If x*y= (x + 3)? (y -1), then the value of 5 * 4 is (1) 192 (2) 182 (3) 180 (4) 172 | 9 |

123 | Rs. 69 were divided among 115 students so that each girl gets 50 paise less than a boy. Thus each boy received twice the paise as each girl received. The no. of girls in the class is | 9 |

124 | ( A^{prime} ) s salary is same as 4 times ( B^{prime} s ) salary. If together they earn Rs. 3,750 a month, find the salary of each. A. ( A ) ‘s = Rs. ( 3000 ; B ) ‘s = Rs. 750 B. ( A^{prime} ) ‘s ( = ) Rs. ( 2000 ; B ) ‘s = Rs. 800 c. ( A ) ‘s ( = ) Rs. ( 2500 ; B ) ‘s ( = ) Rs. 900 D. ( A ) ‘s = Rs. ( 4500 ; B ) ‘s = Rs. 1000 | 9 |

125 | Solve the equations simultaneously to find the value of ( h ) ( 3 h-j=7 ) and ( 2 h+3 j=1 ) ( A cdot 2 ) B. ( c cdot 4 ) D. 3 | 9 |

126 | 8. When we divide 4500 into two parts such that 5% of the first part is equal to 10% of the second part, then the first part and second part is 3000, 1500. | 9 |

127 | 54. Two trains are running in op- posite direction with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, the speed of each train (in km/ hour) is (1) 72 (2) 10 (3) 36 (4) 18 | 9 |

128 | Say true or false. Every solution of the equation is a point on the line representing it. A. True B. False | 9 |

129 | Find ( mathbf{x} ) and ( mathbf{y} ) if ( left[begin{array}{cc}mathbf{2} boldsymbol{x} & boldsymbol{x} \ boldsymbol{y} & boldsymbol{3} boldsymbol{y}end{array}right]left[begin{array}{l}mathbf{3} \ mathbf{2}end{array}right]=left[begin{array}{c}mathbf{1} mathbf{6} \ mathbf{9}end{array}right] ) | 9 |

130 | If we add 1 to the numerator and subtract 1 from the denominator a fraction becomes ( 1 . ) It also becomes ( frac{1}{2} ) if we only add 1 to the denominator what is the numerator of the fraction? ( A cdot 2 ) B. 4 ( c cdot 5 ) D. | 9 |

131 | Write each of the following in the form of ( a x+b y+c=0 ) and find the value of ( a, b ) and c (i) ( x=-5 ) (ii) ( y=2 ) (iii) ( 2 x=3 ) ( (i v) 5 y=-3 ) | 9 |

132 | A number is 27 more than the number obtained by reversing its digits. If its unit’s and ten’s digits are ( x ) and ( y ) respectively, write the linear equation representing the above statement | 9 |

133 | 18. A number consists of two digits. The digit in the ten’s place exceeds the digit in the unit’s place by 4. The sum of the digits is of the number. Find the number. | 9 |

134 | What is the value of ( k ) if ( (k, 5) ) is the solution of the simultaneous equations ( 4 x+3 y=19 ) and ( 4 x-3 y=-11 ? ) ( A cdot 4 ) B. ( -1 / 3 ) c. 5 ( D ) | 9 |

135 | The sum of the ages of Anup and his father is ( 100 . ) When Anup is as old as his father now, he will be five times as old as his son Anuj is now. Anuj will be eight years older than Anup is now, when Anup is as old as his father.what are their ages right now. | 9 |

136 | Find the solution of the equation ( x+ ) ( 2 y=6 ) from the options given below: B. (0,2),(6,0),(2,2) and (4,1) D. (0,3),(6,0),(1,2) and (4,1) | 9 |

137 | 65. When we draw the graphs of the equations x + y = 6 and 2x + 3y = 16 on the same graph paper, the coordinates of the point where the two lines intersect are (1) (-3, 6) (2) (-2, 0) (3) (2, 4) (4) (1, 3) | 9 |

138 | The cost of notebook is twice the cost of a pen. Write a linear equation in two variable to represent this statement | 9 |

139 | Express the linear equation in the form ( a x+b y+c=0 ) and indicate the value of ( a, b ) and ( c ) in each case: ( x-frac{y}{5}-10=0 ) | 9 |

140 | Solve in positive integers: ( 23 x+25 y=915 ) This question has multiple correct options A. ( x=15, y=6 ) B. ( x=30, y=9 ) c. ( x=5, y=32 ) D. ( x=10, y=8 ) | 9 |

141 | The difference between two positive integers is ( 75 . ) The ratio of these integers is ( 7: 4 . ) Find the integers. | 9 |

142 | 52. The sum of the numerator and denominator of a positive fraction is 11. If 2 is added to both nu- merator and denominator, the fraction is increased by 4. The difference of numerator and de- nominator of the fraction is (1) 5 (2)3 (3) 1 (4) 9 | 9 |

143 | 13. A lady has 25 p and 50 p coins in her purse. If in all she has 40 coins totalling 7.12.50, find the number of coins of each type she has. | 9 |

144 | 12. The perimeter of a rectangle is 40cm. The ratio of its side is 2:3. Find its length & breadth. | 9 |

145 | 3. An alloy of silver and gold weighs 90 on in air and 34 min a loud. Assuming that silver loses one-tenth of its weight in the liquid and that gold loses one-nineteenth of is weight. Find the weight of each metal in the alloy | 9 |

146 | Solve ( 2 x+3 y=11 ) and ( 2 x-4 y=-24 ) | 9 |

147 | If point (3,0) lies on the graph of the equation ( 2 x+b y=k, ) then the value of ( boldsymbol{k} ) is : ( mathbf{A} cdot mathbf{6} ) B. 3 ( c cdot 2 ) D. | 9 |

148 | 5. The sum of two numbers is 90 and the greater number exceeds thrice the smaller number by 14. The number is (a) 18,72 (b) 19,71 (c) 20,70 (d) 15,75 | 9 |

149 | Find the solution for the following equations: ( frac{5}{2 x}+frac{2}{3 y}=7 ; frac{3}{x}+frac{2}{y}= ) ( mathbf{1 2} quad(boldsymbol{x} neq mathbf{0}, boldsymbol{y} neq mathbf{0}) ) | 9 |

150 | The length of a rectangle exceeds its breadth by 4 cm. If length and breadth are each increased by 3 cm, the area of the new rectangle will be 81 cm? more than that of the givne rectangle. Find the length and breadth of the given rectangle. | 9 |

151 | The points (7,2) and (-1,0) lie on a line A. ( 7 y=3 x-7 ) B. ( 4 y=x+1 ) c. ( y=7 x+7 ) D. ( x=4 y+1 ) | 9 |

152 | Find out which of the following equations have ( x=2, y=1 ) as a solution: ( 2 x-3 y=1 ) | 9 |

153 | If three times the larger of two numbers is divided by the smaller, we get 4 as the quotient and 8 as the remainder. If five times the smaller is divided by the larger, we get 3 as the quotient and 5 as the remainder. Find the numbers. | 9 |

154 | Find four different solution of ( 4 x+y=9 ) | 9 |

155 | Solve. ( 4 x-4=5+x ) | 9 |

156 | 1. Find the value of p’, ifx=2 and y=1. is a solution of the equation 2x + 3y=p | 9 |

157 | The coach of a cricket team buys 7 bats and 6 balls for Rs. 3800 . Later, she buys 3 bats and 5 balls for Rs. 1750 . Find the ( operatorname{cost} ) of each bat and each ball | 9 |

158 | In the given equation ( boldsymbol{a}=frac{boldsymbol{2}}{boldsymbol{3}} boldsymbol{b}+mathbf{5} ) At what value ( a ) becomes equal to ( b ) ? A . 5 B. 7 c. 10 D. 15 | 9 |

159 | If ( (4)^{x+y}=1 ) and ( (4)^{x-y}=4 ) then the values of ( x ) and ( y ) will be respectively A ( cdot frac{1}{2} ) and ( -frac{1}{2} ) B ( cdot frac{1}{2} ) and ( frac{1}{2} ) c. ( -frac{1}{2} ) and ( -frac{1}{2} ) D. ( -frac{1}{2} ) and ( frac{1}{2} ) | 9 |

160 | On the first day of the sale of tickets of a drama, in all 35 tickets were sold. If the rates of the tickets were Rs. 20 and Rs. 40 per ticket and the total collection was Rs. ( 900, ) find the number of tickets sold of each rate. | 9 |

161 | Divide 32 into two parts such that 5 times one part added to 6 times the other part gives 164 | 9 |

162 | A car takes 1 hour less to cover a distance of ( 200 mathrm{km} ) if its speed is increased by ( 10 mathrm{km} / mathrm{hr} ), than its usual speed. What is the usual speed of the car. | 9 |

163 | Show that ( x=1, y=3 ) satisfy the linear equation ( 3 x-4 y+9=0 ) | 9 |

164 | Rakesh went to a stationary shop to purchase a total of 38 pens, erasers and sharpeners. He purchased at least 11 items of each. He purchased more sharpeners than erasers and more erasers than pens. How many pens did he purchase? A . 11 B. 12 c. 13 D. 14 | 9 |

165 | Evaluate: ( boldsymbol{x}+boldsymbol{y}=mathbf{4} ; mathbf{2} boldsymbol{x}-mathbf{5} boldsymbol{y}=mathbf{1} ) | 9 |

166 | Solving ( frac{mathbf{2}}{boldsymbol{x}}+mathbf{3} boldsymbol{y}=-mathbf{3} ) and ( boldsymbol{y}-boldsymbol{4} boldsymbol{x}=frac{mathbf{7}}{mathbf{3}} ) gives ( (mathbf{x}, mathbf{y}) ) ( mathbf{A} cdotleft(-frac{1}{2}, 3right) ) B ( cdotleft(-1, frac{1}{3}right) ) c. ( left(-frac{1}{2}, frac{1}{3}right) ) D ( cdotleft(-2, frac{1}{3}right) ) | 9 |

167 | Solve the following systems of equations. ( boldsymbol{x}+mathbf{2} boldsymbol{y}-boldsymbol{6}=mathbf{0},|boldsymbol{x}-mathbf{3}|-boldsymbol{y}=mathbf{0} ) | 9 |

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