Linear Equations In Two Variables Questions

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
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
A ( . y=8 x+7 )
В. ( y=8 x-7 )
c. ( y=8 x+15 )
D. None of these

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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