LINEAR EQUATION IN ONE VARIABLE
I. Choose the correct option.
1.Solve
the equation:
(A) 1
2.If
(B) 2
.
(C) 3
(D) 4
two third of a number is increased by 9, the sum will be 19 find the number.
(A) 15
3.Solve
(B) 17
the equation:
(A)
4.Solve
(B)
(B) 3
(B)
(B) -1
(D)
.
(C) 4
(D) 5
(C)
(D)
.
(C) -2
the equation:
(A) 4
8.Solve
(C)
the equation:
(A) 1
7.Solve
.
the equation:
(A)
6.Solve
(D) 5
the equation:
(A) 2
5.Solve
(C) 20
(B) 8
the equation:
(A) -52
(B) +52
(D) 2
.
(C) 10
(D) 12
.
(C) 63
(D) 64
9.If
is subtracted from a number and the difference is multipled by 4, the result is
5. Find the number.
(A)
(B)
10.Solve
(A)
(C)
the equation:
(B)
.
(C)
11.If
(D)
then value of y is:
(A) 2
12.Value
(D) 4
(B)
(C) 3
(D) -6
of x in 2(6x - 5) = -(3x + 1) + 6
(A) 1
13.Solution
(B) 2
(C) 3
of x in
(A)
(B)
14.Solution
(D) 4
(C) 2
(D)
for x in 4(2x - 3) + 5(3x - 4) =14.
(A) 4
(B) 3
(C) 2
(D) 5
15.One
of the angle of the triangle is equal to the sum of the other two .If the ratio
of the other two angle is 2:3 then the angles ( in degree) are.
(A) 90, 36, 54
(B) 40, 50, 90
(C) 30, 60, 90
(D) 38, 57, 85
16.Two
numbers are in ratio 5 : 8. If the sum of the numbers is 182, then the
numbers are:
(A) 70, 112
(B) 80, 102
(C) 58, 124
(D) 30, 66
17.Four-fifth
of a number is greater than three-fourth of the number by 4. The
number is:
(A) 12
(B) 64
(C) 80
(D) 102
18.A
two digit number whose sum of digits is 14. If 36 is added to the number, its
digits are interchanged. The number is:
(A) 68
19.Two
(B) 95
(C) 86
(D) 59
complementary angles differ by 16º. The angles are:
(A) 53o, 37o
(B) 56o, 40o
(C) 62o, 28o
(D) 59o, 31o
20.Two
numbers are in ratio 6 : 7. If the sum of the numbers is 169, then the
numbers are:
(A) 78, 91
21.Two
(B) 80, 89
(C) 65, 104
(D) 104, 65
complementary angles are equal, each angles will be:
(A) 45o
(B) 60o
(C) 90o
(D) 55o
22.The
denominator of a rational number is greater than its numerator by 3, if 3 is
subtracted from the numerator and 2 is added to the denominator the new
number becomes
(A) 6/8
. The original number is:
(B) 5/8
(C) 7/8
(D) 9/8
23.The
sum of the digits of a two digit number is 15, if the number formed by
reversing the digits is less than the original number by 27, the original number
is:
(A) 96
(B) 69
(C) 76
(D) 84
24.The
length of a rectangle is more than its breadth by 9 cm. If the length and
breadth are each increased by 3 cm, the area of new rectangle will be 64cm 2
more than that of the given rectangle. Then the length and breadth of the
rectangle are:
(A) l = 10cm, b = 6 cm
(B) l = 0 cm, b = 15 cm
(C) l = 17cm , b= 8 cm`
(D) l = 21 cm, b = 30 cm
25.A
steamer goes down stream and covers the distance between 2 ports in 4
hours while it covers the same distance up stream in 5 hours. If the speed of
the stream is 2 km/h, find the speed of the steamer in still water.
(A) 9 km/h
(B) 11km/h
(C) 21 km/h
(D) 18 km/h
26.Two
years ago, Dilip was three times as old as his son and two years hence twice
his age will be equal to five times that of his son. Find their present ages:
(A) 10 yrs, 20 yrs
(B) 15 yrs, 19 yrs
(C) 14 yrs, 38 yrs
(D) 35 yrs, 60 yrs
27.Divide
184 into two parts such that one third of one part may exceed one
seventh of the other part by 8. The numbers are:
(A) 46 , 138
28.The
(B) 32 , 152
(C) 64 , 120
(D) 72 , 112
sum of first three consecutive multiples of a number is 162, the number is:
(A) 16
(B) 22
(C) 25
(D) 27
29.If
we subtract 2/5 from a number and divide the result by 8/3, we get 11/4, the
number is:
(A) 16/15
(B) 22/15
(C) 27/32
(D) None of these
30.The
ratio of the present ages of Devang and Devesh is 4 : 7. Six years later, the
sum of their ages is 34 years. The present ages of Devang and Devesh is:
(A) 12 years, 21 year
of these
(B) 8 years, 14 years (C) 14 years, 20 years (D) None
31.The
perimeter of a rectangular field 154 meter, its length is 2 meter more than
twice its breath. If a 2 meter wide path is around the field, then the length of
rectangular path is:
(A) 52 m
(B) 29 m
(C) 48 m
(D) 56 m
32.The
denominator of a rational number is greater than its numerator by 5. If the
numerator is increased by 12 and denominator decreased by 3, the obtained
rational number is 5/3. The rational number is:
(A) 3/5
(B) 13/18
(C) 8/3
II. Solve the following.(2M)
1.Solve
the equation:
.
(D) None of these
2.Sum
of two numbers is 52, if second number is 10 more than first.
Find the numbers.
3.Sum
of three consecutive even integers is 270. Find the integers.
4.Sum
of three consecutive integers is 246. Find the integers.
5.Sum
of three consecutive multiples of 7 is 777, find the numbers.
6.The
ratio of two complementary angles is 4 : 5. Find these angles and ratio of their
supplementary angles.
7.A
mother is 24 years older than her son. After 4 years ,the age of mother will be
three times the age of son. Find the present ages of mother and son.
8.The
ages of suman and neelam are in the ratio 3:4,4 years ago,their ages were in
the ratio 5:7.Find their ages?
III. Solve the following.(3M)
1.If
, then the value of x is:
2.If
, then value of x is:
3.The
solution of
4.The
solution of the equation
(A) -1
5.The
(B) 3
solution of the equation
(A) -11/ 9
6.Solve
a)
7.The
is:
(B) -13/ 4
is:
(C) - 2
(D) 5
is:
(C) -9/ 14
(D) - 2/ 13
the following problems:
=2
b)
difference between two positive integers is 51. The quotient when one integer
is divided by the other is 4. Find the two integers.
8.The
denominator of a rational number is greater than its numerator by 3. If
numerator and denominator are increased by 1 and 4 respectively, the numerator
obtained is
. Find the rational number.
IV. Solve the following.(4M)
1.Solve
=
2.The
numerator of a rational number is 2 more than 3 times the denominator . If
the denominator is increased by 5 and numerator is decreased by 5, the number
obtained is
. Find rational number.
3. Keerthi has only Rs 100 and Rs 500 /- currency notes in her purse. The total money
in the purse is Rs5000. If the number of Rs 100 is one more than twice the number of
Rs 500 notes, find the number of each type of notes in keerthi’ purse.
4. Karan has three gift boxes of different sizes. The first box is 10cm longer than the
third box and the second box is 5cm longer than the third box. If the total length of
the three boxes is 75cm, then find the length of each box.
5. Solve for x and verify the following equation:
𝑥+𝑃 𝑥−𝑃
=
𝑝+𝑞 𝑝−𝑞
6. The sum of the digits of a 2-digit number is 13. If the number obtained by inter
changing the digits exceeds the original number by 27, find the number.
7. The sum of the digits of a 2-digit number is 12. The given number exceeds the
number obtained by inter changing the digit by 36, find the given number.
8. Mr. Khan won a cash prize of certain amount in the jack pot of a carnival. He gave
1
half of this money and an additional amount of Rs 10,000/ to his wife. He also gave 3
of the money received and an additional amount of Rs 3000/- to his son. If his wife
got double the amount his son got , find the amount of money Mr khan won in the
jack pot.
5−7𝑦
−8
9.Solve the following equation: 2+4𝑦 = 7
10.Solve
(5𝑥−7)−(2𝑥+3)
6𝑥+11
=
8
3