Linear Equations in One variable Test

Result

Linear Equations in One variable Test - 6

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Weekly Quiz Competition

Question 1
1 / -0

Find the value of x in .

A
7

B
6

C
5

D
3

Solution

10(6 - 2x) = 7(2x - 6)
60 - 20x = 14x - 42
20x + 14x = 60 + 42
34x = 102
x = 3
Question 2
1 / -0

A number is 26 more than the sum of its quarter, one-third and one-fifth. What is the number?

A
180

B
150

C
120

D
108

Solution

Let the number be x.
According to the question,

13x = 1560
x = 120
Option (3) is correct.
Question 3
1 / -0

If of a number is 64 less than the original number, then the number is

A
64

B
80

C
88

D
96

Solution

Let the number be x.
So, as per the information,

4x = 320
x = 80
Option (2) is correct.
Question 4
1 / -0

Directions: Find the value of x in 3(7x + 2) - 4(4x- 1) = 8(3x + 4) - 4(5x- 4).

A
0

B
16

C
38

D
None of these

Solution

3(7x + 2) - 4(4x - 1) = 8(3x + 4) - 4(5x - 4)
21x + 6 - 16x + 4 = 24x + 32 - 20x + 16
21x - 16x - 24x + 20x = 32 + 16 - 6 - 4
x = 38
Question 5
1 / -0

The number 323 is divided into two parts in ratio 7 : 10. If the smaller part is increased by 5 times and bigger part is increased by 7 times, then what will be the sum of the two parts?

A
1989

B
2992

C
2318

D
2198

Solution

Let the two parts be 7x and 10x.
So, as per the information given in the question,
7x + 10x = 323
17x = 323
x = 19
Smaller part = 7x = 133
Bigger part = 10x = 190

Smaller part after increase = 133 × 6 = 798
Bigger part after increase = 190 × 8 = 1520
Required sum = 798 + 1520 = 2318
Option (3) is correct.
Question 6
1 / -0

If of a number is 78 more than the original number, then the number is

A
246

B
215

C
195

D
202

Solution

Let the number be x.
So, as per the information given in the question,

x = 195
Question 7
1 / -0

The sum of two numbers is same as their product. If one of the numbers is , then what is the other number?

A

B

C

D

Solution

Let the number be x.

2.6x = 3.6

x =

x =
Question 8
1 / -0

A number whose 8^th part exceeds its 9^th part by 2, is

A
144

B
216

C
288

D
360

Solution

Let the number be x.

x = 144
Option (1) is correct.
Question 9
1 / -0

A number consists of two digits whose sum is 11. If 45 is added to the original number, then its digits are interchanged. Then, the original number is

A
58

B
38

C
32

D
28

Solution

Let the digit at the units place be x.
Then, the digit at the tens place will be (11 - x).
Therefore, original number = 10(11 - x) + x
= (110 - 10x) + x
= 110 - 9x

Now, after interchanging the digits, the number formed = 10(x) + (11 - x)
= 10x + 11 - x
= 9x + 11

Now, according to the question,

110 - 9x + 45 = 9x + 11
110 + 45 - 11 = 9x + 9x
144 = 18x
x = 8

Therefore, original number is 110 - 9x.
= 110 - 72
= 38
Option (2) is correct.
Question 10
1 / -0

The numerator of a rational number is 4 less than its denominator. If 3 is added to the denominator and 3 is subtracted from the numerator, then the new number becomes. The original number is

A

B

C

D

Solution

Let the numerator be x.
Then, the denominator = x + 4
Therefore, the original rational number =
According to the information given in the question,

7x - 21 = 2x + 14
7x - 2x = 14 + 21
5x = 35
x = 7
So, required rational number is
Option (1) is correct.
Question 11
1 / -0

If , then find the value of p.

A

B

C

D

Solution

-64p - 8 = 6p - 3

-8 + 3 = 6p + 64p

-5 = 70p

p =

Option (2) is correct.
Question 12
1 / -0

A two-digit number is less than 40 but greater than 30. The sum of its digits is half of their product. What is the number?

A
36

B
33

C
32

D
31

Solution

Since the two-digit number is less than 40 and greater than 30, the tens digit will be 3.

Let the digit at the ones place be x.
According to the question,

3 + x =
6 + 2x = 3x
6 = x
Or x = 6
So, the number can be 36.
Option (1) is correct.
Question 13
1 / -0

Which of the following can be two parts of 68, if ^th of one part is equal to^th parts of other?

A
61 and 7

B
51 and 17

C
50 and 18

D
52 and 16

Solution

Let one part be x and other be 68 - x.
According to the question, we have
x = (68 - x)
= -
+ =
=
x =
x = 51
Other part = 68 - 51 = 17
Option (2) is correct.
Question 14
1 / -0

If the angles of a quadrilateral are in ratio 2 : 3 : 6 : 7, then find the difference between the largest and the smallest angles of the quadrilateral.

A
120°

B
100°

C
90°

D
80°

Solution

Let the angles of quadrilateral be 2x, 3x, 6x and 7x.
2x + 3x + 6x + 7x = 360°
18x = 360°
x = 20°
So, angles of quadrilateral = 2 x 20 = 40°
3 x 20 = 60°
6 x 20 = 120°
7 x 20 = 140°
So, the difference between the largest and the smallest angle = 140 - 40 = 100°
Option (2) is correct.
Question 15
1 / -0

One-third of a number when subtracted from a number itself, gives 34. The number is

A
24

B
33

C
51

D
58

Solution

Let the number be x.
According to question, we have
x -x = 34
2x = 3 x 34
x = 51
Option (3) is correct.
Question 16
1 / -0

Of the classes A and B in a school, 12% of the total students are in class A and the rest in class B. The difference between the number of students in classes A and B is 152. Find the total number of students in both the classes.

A
100

B
200

C
300

D
400

Solution

Let the total students be x.
Number of students in class A = 12% of x = 0.12x
Now, number of students in class B = x - 0.12x = 0.88x
Now, 0.88x - 0.12x = 152
0.76x = 152
x = 200
Option (2) is correct.
Question 17
1 / -0

Amit is 24 years older than Rohit. 2 years hence, his age will be twice the age of Rohit. Find the present age of Rohit.

A
22 years

B
21 years

C
20 years

D
19 years

Solution

Let the present age of Rohit be x.
Age of Amit = x + 24
Two years hence,
x + 24 + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22
Option (1) is correct.
Question 18
1 / -0

In a school, one third students like apples, one fourth like oranges and one fifths like grapes. How many students do not like fruits, if total 240 students are in school?

A
10

B
20

C
52

D
54

Solution

Students who like apples =
Students who like oranges =
Students who like grapes =
Total = 80 + 60 + 48 = 188
Students who do not like fruits = 240 - 188 = 52
Option (3) is correct.
Question 19
1 / -0

P is two years older than Q and Q is twice as old as R. If combined age of all of them is 27, then find the age of Q.

A
10 years

B
12 years

C
13 years

D
14 years

Solution

Let R's age be x years.
Then, Q's age = 2x years
P's age = (2x + 2) years
As per the given information in the question, we have
(2x + 2) + 2x + x = 27
5x = 25
x = 5
Hence, Q's age = 2x = 10 years
Option (1) is correct.
Question 20
1 / -0

A boat travels a certain distance at a speed of 11 km/hr upstream and at 5 km/hr downstream. Find the speed of boat in still water.

A
7 km/hr

B
8 km/hr

C
9 km/hr

D
10 km/hr

Solution

Let the speed of boat in still water be a.
And let the speed of river be b.
Upstream speed = a - b
Downstream speed = a + b
So, a - b = 5 (Upstream speed)
a + b = 11 (Downstream speed)

Adding these equations, we get
2a = 16
a = 8
Speed of boat in still water = 8 km/hr
Question 21
1 / -0

Directions: Fill in the blanks.

(i) x² + 1 = 5 is a ____ equation.
(ii) If a and b are negative integers, then solution of ax = b has to be always ____.
(iii) Value of x for which 3x - 4 and 2x + 1 becomes equal is ___.
(iv) A linear equation in one variable has _____ solution(s).

A

(i) (ii) (iii) (iv)

Non-Linear positive 5 one

B

(i) (ii) (iii) (iv)

Linear negative 5 one

C

(i) (ii) (iii) (iv)

Linear positive 4 one

D

(i) (ii) (iii) (iv)

Non-Linear positive 5 two

Solution

(i) x² + 1 = 5 is not a linear equation.
So, x² + 1 = 5 is a Non-linear equation.
As power of the variable is 2.

(ii) If ax = b, then x = b/a. Since a and b are negative, x would be positive.

(iii) 3x - 4 and 2x + 1 are equal.
3x - 4 = 2x + 1
x = 5

(iv) A linear equation in 1 variable has only 1 unique solution.

Option (1) is correct.
Question 22
1 / -0

Which of following statements is/are correct?

Statement (1): x = is the solution of .

Statement (2): x = is the solution of .

A
Only statement 1

B
Only statement 2

C
Both of these

D
Neither of these

Solution

Statement (1):

28x + 6 = 3x + 3
25x = -3
x =

Statement (2):

8x + 12 + 15x + 3 = 144
23x + 15 = 144
23x = 129

x =

Option (1) is correct.
Question 23
1 / -0

Directions: State 'T' for true and 'F' for false.

I. Length of a rectangle is 10 m more than breadth. Perimeter of rectangle is 80 m. The dimensions of that rectangle is 15 cm and 25 cm.
II. Length of a rectangle exceeds its breadth by 3 cm. If the length and breadth are each increased by 2 cm, then the area of new rectangle will be 70 sq.cm more than that of the given rectangle. Length and breadth of the given rectangle are 18 cm and 15 cm.
III. Four-fifth of a number is more than three-fourth of that number by 5. That number is 120.

A

I II III

T T T

B

I II III

T T F

C

I II III

T F T

D

I II III

F T T

Solution

I. Let b = x, then l = x + 10
Perimeter = 2(l + b) = 2(x + 10 + x)
Given, 2(x + 10 + x) = 80
2(10 + 2x) = 80
10 + 2x = 40
2x = 30
x = 15
Breadth = 15 cm and length = 25 cm

II. Length = Breadth + 3
Let b = x
l = x + 3
Area = x(x + 3) = x²+ 3x
New b = x + 2
New l = x + 3 + 2 = x + 5
New area = (x + 5)(x + 2) = x²+ 7x + 10
x²+ 7x + 10 - x²- 3x = 70
4x + 10 = 70
4x = 60
x = 15
b = 15 cm
l = 18 cm

III. Let number be x.

16x - 15x = 20 x 5
x = 100

Option (2) is correct.
Question 24
1 / -0

Which of the following statements is incorrect?

A. I have Rs. 300 with me in form of 1 rupee coins, 2 rupee coins and 5 rupee coins. Number of 2 rupee coins is 3 times the number of 5 rupee coins. Total number of coins is 160. So, I have twenty 5 rupee coins.
B. Cost of a pencil is 25 paise more than cost of an eraser. Cost of 8 pencils and 10 erasers is Rs. 12.80. Cost of one eraser is 50 paise.
C. Amit's father is 49 years old. He is 5 years older than four times Amit's age. Amit is 11 years old.
D. If sum of two consecutive even numbers is 38, then those numbers are 18 and 20.

A
B

B
A

C
C

D
D

Solution

(A) Let Rs. 5 coins = x
Rs. 2 coins = 3x
Re. 1 coins = 160 - (x + 3x) = 160 - 4x
Total money = Rs. 300
5x + 2 × 3x + (160 - 4x) = 300
5x + 6x + 160 - 4x = 300
7x + 160 = 300
7x = 140
x = 20
Correct statement.

(B) Cost of eraser = x
Cost of pencil = x + 25
8 × (x + 25) + 10x = 12.80 × 100
8x + 200 + 10x = 1280
18x = 1080
x = 60
Cost of the eraser is 60 paise.
Wrong statement.

(C) Let Amit be x years old.
Father's age = 4x + 5
4x + 5 = 49
4x = 44
x = 11
Correct statement.

(D) x + x + 2 = 38
2x + 2 = 38
x = 18
Numbers are 18 and 20.
Correct statement.

Option (1) is correct.

Question 25

1 / -0

Directions: Match the following.

	Column I	Column II
P.	If , then find x.	(i) 4
Q.	If , then x = ?	(ii)
R.	If , then x = ?	(iii) 1
S.	If , then x = ?	(iv) 2

P Q R S

(ii) (i) (iii) (iv)

P Q R S

(i) (ii) (ii) (iv)

P Q R S

(ii) (iv) (i) (iii)

P Q R S

(ii) (i) (iv) (iii)

Solution

^(P)

20x + 12 = 30x - 15
10x = 27

x =

(Q)

8(21 - 5x) = 68 - 15x
168 - 40x = 68 - 15x
25x = 100
x = 4

(R)

x + 3 + 6 = 12x - 2
11x = 11
x = 1

(S)

3 + 7x = 17
7x = 14
x = 2

Option (1) is correct.

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Linear Equations in One variable Test - 6

Result

Linear Equations in One variable Test - 6

Score

-

Rank

-

SHARING IS CARING

Question 1

7

6

5

3

Solution

Question 2

180

150

120

108

Solution

Question 3

64

80

88

96

Solution

Question 4

0

16

38

None of these

Solution

Question 5

1989

2992

2318

2198

Solution

Question 6

246

215

195

202

Solution

Question 7

Solution

Question 8

144

216

288

360

Solution

Question 9

58

38

32

28

Solution

Question 10

Solution

Question 11

Solution

Question 12

36

33

32

31

Solution

Question 13

61 and 7

51 and 17

50 and 18

52 and 16

Solution

Question 14

120°

100°

90°

80°

Solution

(i) (ii) (iii) (iv)

Non-Linear positive 5 one

(i) (ii) (iii) (iv)

Linear negative 5 one

(i) (ii) (iii) (iv)

Linear positive 4 one

(i) (ii) (iii) (iv)

Non-Linear positive 5 two

I II III

T T T

I II III

T T F

I II III

T F T

I II III

F T T