Simple Equations Test

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Simple Equations Test - 10

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Weekly Quiz Competition

Question 1
1 / -0

There are 28 students that you want to arrange in 4 lines. You want equal number of students in each line. If you have to find the number of students, , in each line, then which of the following equations will you use?

A

B

C

D

Solution

Total number of students = Number of lines × Number of students in a line
Question 2
1 / -0

The solution of the equation 20 – 3p = 2 is

A
3

B
4

C
6

D
8

Solution

20 – 3p = 2
18 = 3p
p = 6
Question 3
1 / -0

6 more than thrice a number and then subtracting 5 gives us 25. The number is

A
6

B
8

C
10

D
12

Solution

Let the number be x
3x + 6 – 5 = 25
3x + 1 = 25
3x = 24
x = 8
Question 4
1 / -0

Which of the following equations does not have 6 as its solution?

A
x + 9 = 15

B
18 – x = 12

C
8x = 48

D
= 9

Solution

(1) x + 9 = 15
x = 6

(2) 18 – x = 12
x = 6

(3) 8x = 48
x = = 6
(4) = 9

x = 5
Question 5
1 / -0

Find the smaller part of 174 if it is divided into two parts such that one half of one part may exceed one quarter of the other part by 9.

A
124

B
94

C
70

D
63

Solution

Let the one part be x.
Then, the other part will be 174 - x.
According to the question,

× x = (174 - x) + 9

x =

2x = 210 - x
3x = 210
x = 70
Other part = 174 – 70 =104
Question 6
1 / -0

If , find the value of p.

A

B

C

D

Solution

We have

= 1

4p = (2-p)
4p + p = 2
5p = 2
Question 7
1 / -0

What is the value of x that makes the following expression true?

x + {5 - (-3 - (7 × 2 - 6)} = 15

A
-15

B
-10

C
-1

D
10

Solution

x + {5 - (-3 - (7 × 2 - 6)} = 15
x + {5 - (-3 - (8)} = 15
x + {5 - (-11)} = 15
x + {5 + 11} = 15
x + {16} = 15
x = 15 - 16
x = -1
Question 8
1 / -0

If three-fourth of a number, five-seventh of the same number and three-fifth of the same number are added together, the final result is 56. Find the number.

A

B

C

D

Solution

Let the number be x.

According to the question:
Question 9
1 / -0

There are two supplementary angles which have the difference of 56°. One of these angles is

A
112°

B
118°

C
119°

D
120°

Solution

Let the first angle be x.

Then, the other angle will be (56° + x).

Now, x + (56° + x) = 180°

2x = 180° - 56°

x = 62°

And the second angle = (62° + 56°) = 118°
Question 10
1 / -0

The value of x in (5x + 3) + (6x – ) = x – is

A

B

C
-9

D
5

Solution

(5x + 3) + (6x – ) = x –
Question 11
1 / -0

If (7x + 2) + = 4, find the value of x.

A

B

C

D

Solution

We have (7x + 2) + = 4

21x = 28 - 10

21x = 18

x =
Question 12
1 / -0

If ^th of a number is 56, find^th of the same number.

A
25

B
20

C
42

D
47

Solution

Let the number be x.

Then, ^th of x = 56

Now^th of the number =
Question 13
1 / -0

Solve for x:

+=

A

B

C

D

Solution

+=

=

=

= 5

88 - 16x = 10
88 - 10 = 16x
78 = 16x
39 = 8x

x =
Question 14
1 / -0

Which of the following statements does not hold true in solving the equation 21 + 7x = 7?

A
7x = 7 - 21

B
21 - 7 = -7x

C
+=

D
21 += 7

Solution

The given equation 21 + 7x = 7 can be expressed as 7x = 7 - 21.

Or 21 - 7 = -7x

Or +=
So, we can say that 21 += 7 is the option which doesn't hold true for the given equation.
Question 15
1 / -0

Which of the following equation has solution as x = 5?

A
4x + 10 = 30

B
21x + 6 = 30

C
10x + 8 = 32

D
9x + 12 = 48

Solution

(1) 4x + 10 = 30
4x = 20
x = 5

(2) 21x + 6 = 30
21x = 24
x =

(3) 10x + 8 = 32
10x = 24
x =

(4) 9x + 12 = 48
9x = 36
x = 4
Question 16
1 / -0

Riya's uncle is 5 years older than three times the age of Riya. If age of Riya's uncle is 52 years and riya's age is x yrs. Form an equation to find Riya's age.

A
15x + 5 = 52

B
15x + 3 = 52

C
5x + 3 = 52

D
3x + 5 = 52

Solution

We know that
Riya's age = x yrs
and Riya's Uncle age = 52 yrs
Age of Riya's uncle = (5 + 3x) years
According to the question:
3x + 5 = 52
Question 17
1 / -0

Rohan is a truck driver and works with a logistic company. He is transporting mangoes in two types of boxes, one small and one large. Each large box contains 20 small boxes plus 7 loose mangoes. If the number of mangoes in 1 large box is 67 and number of mangoes in each small box is x, then form an equation which shows the number of mangoes in each small box.

A
20x + 15 = 40

B
15x + 6 = 40

C
20x + 7 = 67

D
20x - 7 = 67

Solution

The number of mangoes in each small box = x
Number of small boxes in a large box = 20
According to the question,
20x + 7 = 67
Question 18
1 / -0

There are some boys and girls standing in a line. The number of girls is 5 less than five times the number of boys in a line. What is the number of boys if the total number of girls is 75?

A
10

B
12

C
14

D
16

Solution

Let the number of boys in the line be x.
According to the question,
5x – 5 = 75
5x = 80
x = 16
Question 19
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There are 60 candidates who appeared for a test. The highest marks scored by a candidate is 6 times the lowest marks plus 12. The candidate who scored the highest got 126 marks and who scored the lowest is p. Form an equation which will help in calculating the lowest marks.

A
6p + 126 = 12

B
6p + 12 = 126

C
12p + 6 = 126

D
12p + 126 = 6

Solution

We know that
Lowest marks scored by a candidate = p
Highest marks scored by a candidate = 126
According to the question,
6p + 12 = 126
Question 20
1 / -0

There are some pizzas on a table and some children are there around the table. If each child eats only one pizza, then one child will be left without getting any pizza. If a pair of children starts eating one pizza only, then there will be one pizza left. Find the number of children and pizzas, respectively.

A
5, 6

B
6, 5

C
8, 9

D
4, 3

Solution

Let n be the number of children.
So, number of pizzas = (n – 1)
If the number of children having each pizza is 2, then the number of pizzas will be .
So, we have

2 + 2 = 2n - n
n = 4
Thus, the number of children is 4 and that of pizzas is (4 – 1), i.e. 3.
Question 21
1 / -0

A number consists of two digits whose sum is 5. If 9 is added to the number, its digits are interchanged. Which of the given steps is/are CORRECT to find the number?

Step 1: Let the units digit be x.
Step 2: Then, tens digit = (5 - x)
Number =
= 50 - 10x + x
= 50 - 9x
Step 3: Adding 9 to the number (50 - 9x), we get 59 – 9x
Step 4: Number with digits interchanged = 10x + (5 - x) = 9x + 5
Step 5: 59 - 9x = 9x + 5
Step 6: Therefore, units digit = 3 and tens digit = 2
Step 7: Hence, number = 23

A
Only step 2

B
Steps 2, 5 and 7

C
Steps 2 and 6

D
All steps are correct.

Solution

All steps are correct as the steps are leading to the correct answer, which is 23.
Question 22
1 / -0

Select the INCORRECT statement.

A
'y exceeds 4 by 8' can be represented as y + 4 = 8.

B
We can add a rational number to an equation.

C
7 is the solution for the equation 9x + 2 = 65.

D
Shifting one term from one side of an equation to another side with a change of sign is known as transposition.

Solution

Statement (1) is incorrect because 'y exceeds 4 by 8' can be represented as y - 4 = 8.
The given statement means y is 8 more than 4.
So, the equation is: y - 8 = 4
We can also write it as: y - 4 = 8.

Question 23

1 / -0

Directions: Choose the correct answers from the table and mark the correct option accordingly.

The sum of two numbers is 84. One is thrice the other.

(a) If the smaller number is m, find the other number.
(b) Find the equation formed.
(c) Find the numbers.

	(a)	(b)	(c)
A.	m + 3	m + 3m = 84	11, 33
B.	3m	m + 3m = 84	21, 63
C.	m - 3	m + 3m = 84	22, 61
D.		m + 3m = 84	24, 60

A

B

C

D

Solution

First number = m
Second number = 3m
According to the question,
m + 3m = 84
4m = 84
m =
m = 21
So, the numbers are 21 and 63.

Question 24

1 / -0

Directions: Choose the correct answers from the table and mark the correct option accordingly.

There are 60 children who all have gathered in a hall. These children have some money with them. Each girl has Rs. 25 and each boy has Rs. 40. If the total amount of money with these 60 children is Rs. 1950 and number of boys is x, then

(i) the equation formed is _______.
(ii) the number of boys is _______.
(iii) the number of girls is _______.

	(i)	(ii)	(iii)
A.	40x + 25(x - 60) = 1950	40	30
B.	40x + 25(60 - x) = 1950	30	20
C.	40x + 25(x - 60) = 1950	40	20
D.	40x + 25(60 - x) = 1950	30	30

A

B

C

D

Solution

Number of boys = x
Then, number of girls = 60 - x
According to the question,
40x + 25 (60 - x) = 1950
40x + 1500 – 25x = 1950
15x = 450
x = 30
Number of boys = 30
So, number of girls = 60 - 30 = 30

Question 25

1 / -0

Match the following:

Column - I	Column - II
P. The age of Rahul's mother is 8 years more than 3 times the age of Rahul. If the age of Rahul's mother is 56, the Rahul's age is	(i) 10
Q. Riya has 12 more pens than 6 times the number of pens that Piya has. Riya has 84 pens. The number of pens with Piya is	(ii) 12
R. Arun and Rohan started collecting different coins for there collection. Arun has 24 more coins than 4 times the number of coins with Rohan. Arun has 64 coins. The number of coins with Rohan is	(iii) 16

	P	Q	R
A	(i)	(ii)	(iii)
B	(i)	(iii)	(ii)
C	(iii)	(ii)	(i)
D	(iii)	(i)	(ii)

A

B

C

D

Solution

(P)
Let Rahul's age be x.
So, Rahul's mother age = 8 + 3x
According to the question,
8 + 3x = 56
3x = 48
x = 16

(Q)
Let the number of pens with Piya be x.
So, number of pens with Riya = 12 + 6x
According to the question,
12 + 6x = 84
6x = 72
x = 12

(R)
Let the number of coins that with Rohan be x.
So, number of coins with Arun = 24 + 4x
According to the question,
24 + 4x = 64
4x = 40
x = 10

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Simple Equations Test - 10

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Simple Equations Test - 10

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SHARING IS CARING

Question 1

Solution

Question 2

3

4

6

8

Solution

Question 3

6

8

10

12

Solution

Question 4

x + 9 = 15

18 – x = 12

8x = 48

= 9

Solution

Question 5

124

94

70

63

Solution

Question 6

Solution

Question 7

-15

-10

-1

10

Solution

Question 8

Solution

Question 9

112°

118°

119°

120°

Solution

Question 10

-9

5

Solution

Question 11

Solution

Question 12

25

20

42

47

Solution

Question 13

Solution

Question 14

7x = 7 - 21

21 - 7 = -7x

+=

21 += 7

Solution

Question 15

4x + 10 = 30

21x + 6 = 30

10x + 8 = 32

9x + 12 = 48

Solution

Question 16

15x + 5 = 52

15x + 3 = 52

5x + 3 = 52