Equations in One Variable Test

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Equations in One Variable Test - 8

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Question 1
1 / -0

If 3x – 15 = 0, find the value of x.

A
– 5

B
15

C
5

D
0

Solution

3x – 15 = 0
Step 1:
Adding 15 on both sides, we get
3x – 15 + 15 = 0 + 15
3x = 15
Step 2:
Dividing both sides by 3, we get

x = = 5 x = 5

Hence, (3) is the correct option.
Question 2
1 / -0

Which of the following is the correct value of x for the equation = 31x?

A
-4

B
4

C
8

D
-8

Solution

= 31x

Step 1:
Multiplying both sides by 3, we get:

x + 368 = 93x

Step 2:
Subtracting 93x from both sides, we get:
x + 368 - 93x = 93x - 93x
x + 368 - 93x = 0
-92x + 368 = 0

Step 3:
Subtracting 368 from both sides, we get:
-92x + 368 - 368 = 0 - 368
-92x = -368

Step 4:
Dividing both sides by -92, we get:

x = 4
Question 3
1 / -0

Determine the value of x that satisfies the equation .

A

B

C

D

Solution

-3 + 8x =
-3 + 8x = 6x

8x = 6x + 3

2x = 3
x =

Question 4

1 / -0

The present age of Sita is three times the present age of Radha. If five years later, Sita's age will be seven years more than twice the age of Radha, then what is the present age of Sita?

12 years

24 years

36 years

48 years

Solution

	Radha	Sita
Present age	x	3x
After 5 years	x + 5	3x + 5

According to the question,
3x + 5 = 2(x + 5) + 7
3x + 5 = 2x + 10 + 7
3x + 5 = 2x + 17
Step 1
Subtract 2x from both sides.
3x + 5 – 2x = 17
x + 5 = 17
Step 2
Subtract 5 from both sides.
x + 5 – 5 = 17 – 5
x = 12
Radha's age is 12 years.
Sita's age is 3x = 3 12 = 36 years.

Question 5
1 / -0

Sahil's mother's age is 10 years more than twice the age of Sahil. If four years ago, his mother's age was 3 times his age, find the present age of Sahil and his mother.

A
Mother's age = 34 years, Sahil's age = 12 years

B
Mother's age = 46 years, Sahil's age = 18 years

C
Mother's age = 36 years, Sahil's age = 18 years

D
Mother's age = 41 years, Sahil's age = 15 years

Solution

Let the present age of Sahil be x years.
Mother's present age = (2x + 10) years

Four years ago,
(2x + 10 - 4) = 3(x - 4)
2x + 6 = 3x - 12
Step 1:
Subtract 3x from both sides.
2x + 6 - 3x = 3x - 12 - 3x
- x + 6 = - 12
Step 2:
Subtract 6 from both sides.
- x = - 12 - 6
- x = - 18
Step 3:
Divide both sides by - 1.
x = 18
Sahil's age = 18 years
Mother's age = 2 18 + 10 = 36 + 10 = 46 years.
Question 6
1 / -0

The breadth and length of a rectangular board are in the respective ratio of 4 : 5. If both the breadth and the length are increased by 8 cm, the new ratio becomes 5 : 6. What are the dimensions of the rectangular board?

A
l = 60 cm , b = 48 cm

B
l = 40 cm , b = 32 cm

C
l = 48 cm , b = 60 cm

D
l = 10 cm, b = 8 cm

Solution

Let the breadth of the board be 4x.
So, the length of the board = 5x

Cross-multiplication gives:
6(4x + 8) = 5(5x + 8)
24x + 48 = 25x + 40
24x + 8 = 25x
x = 8
Breadth = 4x = 4 8 = 32 cm
Length = 5x = 5 8 = 40 cm
Question 7
1 / -0

If 15 is subtracted from 15 times a number, then the result is 30 more than 12 times the number. What will be 3 more than three times this number?

A
48

B
12

C
18

D
45

Solution

Let the number be x.
According to the question:
15x – 15 = 30 + 12x
15x – 12x = 30 + 15
3x = 45
x = = 15
3x + 3 = 3 15 + 3
= 45 + 3 = 48
Question 8
1 / -0

A car covers a distance from station A to B with a certain speed. If its speed is increased by 2 km/hr, then it will cover the same distance in 4 hours. It will cover the same distance in 5 hours if its speed is decreased by 2 km/hr. What is the original speed of the car?

A
16 km/hr

B
18 km/hr

C
20 km/hr

D
22 km/hr

Solution

Let the original speed be x km/hr.
According to the question,
(x + 2) 4 = (x – 2) 5 (D = S t)

4x + 8 = 5x – 10
x = 18 km/hr
Question 9
1 / -0

Half of the students in a class were studying Maths and three times the one-fourth of the remaining were studying Biology. If the rest of the 9 students were studying History, how many students were there in the class?

A
72

B
36

C
8

D
17

Solution

Let the number of students be x.
Students studying Maths =
Remaining students =
=
Students studying Biology =
=
According to the question,

Or

– x = – 9 8
x = 72
Total number of students in the class is 72.
Question 10
1 / -0

In a right-angled triangle, the altitude is three-fourth the base of the triangle. If the altitude is increased by 5 cm and the base is increased by 4 cm, then the sum of new altitude and base becomes 2 more than twice the sum of the old base and altitude. What was the original length of the altitude?

A
4 cm

B
3 cm

C
7 cm

D
8 cm

Solution

Let the old base be b cm.
Old altitude = b cm
According to the question,
New base = b + 4
New altitude = b + 5
Now, 2(b + b) + 2 = b + 4 + b + 5
2(b + b) - (b + b) + 2 = 9
b + b = 9 - 2

b = 4
Altitude = 4 x = 3 cm
Question 11
1 / -0

For a given triangle ABC, the length of BC is twice that of AB and length of AC is thrice that of AB. If 5 cm is added to the length of AB, 7 cm is added to length of BC and 6 cm is added to the length of AC, then sum of all the new sides will become 6 cm more than twice the sum of the original sides. What is the original length of BC?

A
6 cm

B
2 cm

C
4 cm

D
1 cm

Solution

For ABC,
AB = x cm
BC = 2x cm
AC = 3x cm
Then sum = AB + BC + CA
= x + 2x + 3x = 6x
Now, new sides will be
AB = (x + 5) cm
BC = (2x + 7) cm
AC = (3x + 6) cm
New sum = (x + 5) + (2x + 7) + (3x + 6)
= 6x + 18
According to the question,
6x + 18 = 2(6x) + 6
6x + 18 = 12x + 6
6x – 12x = 6 – 18
– 6x = – 12
6x = 12
x = 2
Original length of BC = 2x cm = 2 2 cm = 4 cm
Question 12
1 / -0

In an examination, the ratio of Rahul's correct answers to his incorrect answers was 7 : 5. If the number of correct answers was 8 more than the incorrect answers, then how many questions in all did he attempt in the exam?

A
36

B
52

C
48

D
56

Solution

Let the number of Rahul's correct answers be 7x.
Incorrect answers = 5x
According to the question,
7x = 5x + 8
Step 1
Subtract 5x from both sides.
7x – 5x = 5x + 8 – 5x
2x = 8
Step 2
Divide both sides by 2.
x =
x = 4
Correct answers = 7x = 28
Incorrect answer = 5x = 20
Total questions attempted by Rahul = 28 + 20 = 48
Question 13
1 / -0

The present age of Sham is 3 more than the present age of Ram. If after 5 years, twice the age of Ram and the age of Sham will add up to give 69, then what is the present age of Sham?

A
51 years

B
17 years

C
29 years

D
20 years

Solution

Let present age of Ram be x years.
Present age of Sham will be x + 3 years.
After 5 years,
2(x + 5) + (x + 3 + 5) = 69
2x + 10 + x + 8 = 69
3x + 18 = 69
3(x + 6) = 69
Step 1
Dividing both sides by 3.
x + 6 =
x + 6 = 23
Step 2
Subtracting 6 from both sides.
x + 6 – 6 = 23 – 6
x = 17
Age of Ram = 17 years
Age of Sham = (17 + 3) = 20 years
Question 14
1 / -0

If the sum of three consecutive integers is 72, then which of the following numbers is the greatest among them?

A
23

B
24

C
25

D
26

Solution

Let one number be x.
Then, other numbers will be x + 1 and x + 2.
According to the question,
x + x + 1 + x + 2 = 72
3x + 3 = 72
3(x + 1) = 72
x + 1 = = 24
x = 24 – 1 = 23
The numbers will be 23, 24, 25.
The greatest number obtained is 25.
Question 15
1 / -0

The sum of length and breadth of a rectangle is 12 cm. If five times the length and seven times the width makes a total of 70 cm, what is the area of the rectangle?

A
50 cm²

B
65 cm²

C
70 cm²

D
35 cm²

Solution

Let the length be x cm.
Then, breadth will be (12 – x) cm.
According to the question,
5x + 7(12 – x) = 70
5x + 84 – 7x = 70
– 2x + 84 = 70
– 2x = 70 – 84
– 2x = – 14
x = 7
Length = 7 cm
Breadth = (12 – 7) = 5 cm
^{_{Product =}_{b = 7}_{5 = 35 cm}2}