Linear Equations in One variable Test

Result

Linear Equations in One variable Test - 7

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Question 1
1 / -0

Solve for x:

A

B

C

D

Solution

80x - 30 = 48x + 36

40x - 15 = 24x + 18

16x = 33

x =
Question 2
1 / -0

A number is 147 more than the average of its quarter, one-fifth and one-tenth. Find the number.

A
160

B
180

C
172

D
162

Solution

Let the number be x.
Quarter of x =
One-fifth of x =
One-tenth of x =
Average of the numbers =
=
=
According to the question,
x = 147 +
Or = 147
x = 180
Question 3
1 / -0

If of a number is 15 less than the original number, then the number is

A
22

B
24

C
25

D
21

Solution

Let the original number be x.

According to the question,

x = x + 15

x = 25
Question 4
1 / -0

Solve for x: 5(2x + 1) + 5(4x - 3) = 7(5x + 2) - 9(5x + 1) + 10x

A
2

B

C
6

D

Solution

We have,
5(2x + 1) + 5(4x - 3) = 7(5x + 2) - 9(5x + 1) + 10x
10x + 5 + 20x - 15 = 35x + 14 - 45x - 9 + 10x
10x + 20x - 35x + 45x - 10x = 14 - 9 + 15 - 5
30x = 15
x = 1/2
Question 5
1 / -0

The number 391 is divided into two parts in the ratio 5 : 12. The product of the two numbers is

A
31,520

B
30,740

C
31,740

D
30,215

Solution

Ratio of two parts = 5 : 12

Smaller of the two numbers = × 391 = 115

Larger of the two numbers = × 391 = 276

So, product of the two numbers = 276 × 115 = 31,740
Question 6
1 / -0

If times a number is 30 more than the original number, then the number is

A
20

B
40

C
45

D
60

Solution

Let the number be 'x'.

According to the question,

x = 45
Question 7
1 / -0

The perimeter of a rectangle is numerically equal to three-fourth of the area of the rectangle. If the length of the rectangle is cm, then its width is

A
24 cm

B
42 cm

C
56 cm

D
62 cm

Solution

Let the width of the rectangle be x cm.
Length of the rectangle = = cm
Area of the rectangle = length × width = × x
Perimeter of the rectangle = 2(length + width) = 2( + x)
= 2x +
So, according to the question,

2x + =
=

=

x = 56 cm
Question 8
1 / -0

A number whose sixth part exceeds its seventh part by 2 is

A
84

B
80

C
75

D
70

Solution

Let the number be x.
According to the question,

x = 84
Question 9
1 / -0

A number consists of two digits, whose sum is 15. If 27 is added to the original number, its digits get interchanged. Find the original number.

A
87

B
78

C
69

D
96

Solution

Let the digit at the units place be x.
So, digit at the tens place = (15 - x)
Original number = 10(15 - x) + x
= 150 - 10x + x
= 150 - 9x

Now, after interchanging the digits, the number will become:
10x + 15 - x = 9x + 15

According to the question,
150 - 9x + 27 = 9x + 15
162 = 18x
x = 9

So, original number = 150 - 9x
= 150 - 9 × 9
= 150 - 81
= 69
Question 10
1 / -0

The denominator of a rational number is smaller than its numerator by 5. If 5 is added to the numerator and 3 is added to its denominator, the number becomes 2. What is the original rational number?

A

B

C

D

Solution

Let the numerator be 'x'.
Then, denominator = x - 5
Original rational number =
According to the question,

On cross-multiplying,
x + 5 = 2x - 4
x = 9
Hence, original number =
=
Question 11
1 / -0

If, then X is equal to

A

B

C

D

Solution

-20X + 2 = 6X + 10

-26X = 8
Question 12
1 / -0

A two-digit number is more than 20 but less than 30. Twice the sum of its digits is thrice their product. What is the number?

A
23

B
21

C
27

D
24

Solution

Since the two-digit number is more than 20 but less than 30, the tens digit will be 2.
According to the question,
Let the ones digit be x.
2(2 + x) = 3(2 × x)
4 + 2x = 6x
4x = 4
x = 1
Hence, the number is 21.
Question 13
1 / -0

Find the two parts of 50 such that ^thof one part is equal to ^rd of the other.

A
35 and 15

B
30 and 20

C
32 and 18

D
26 and 24

Solution

Let one part be x.

Then, other part = 50 - x

According to the question,

9x = 800 - 16x

25x = 800

x = 32

So, other part = 50 - 32 = 18

Hence, the two parts are 32 and 18.
Question 14
1 / -0

If the angles of a triangle are in the ratio 5 : 5 : 8, then the sum of two smaller angles is

A
50°

B
60°

C
80°

D
100°

Solution

Let the angles of the triangle be 5x, 5x and 8x.
Sum of the angles = 180°
Therefore,
5x + 5x + 8x = 180°
18x = 180°
x = 10°

So, the angles are,
5x = 50°
5x = 50°
8x = 80°
Hence, the sum of the two smaller angles is 100°.
Question 15
1 / -0

One-ninth of a number when subtracted from the number itself gives 48. Find the number.

A
50

B
52

C
54

D
45

Solution

Let the number be X.
According to the question,

X = 54
So, the number is 54.
Question 16
1 / -0

Two teams appeared for the final round in a basketball tournament. One team got 71% points and was selected winner by a margin of 63 points. The total points were

A
150

B
130

C
120

D
100

Solution

According to the information given in the question, one of the teams got 71% points. Then, the other got (100 - 71)% = 29% points.

Winning-margin of the winner = 71 - 29 = 42%

Now, let the total points be x.

So, 42% of x = 63

So, total points = 150
Question 17
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Sam has £56. He shares it with his two friends, Jeff and Raghav, such that of the amount received by Jeff is equal to of the amount received by Raghav. Find out the respective amounts received by Jeff and Raghav.

A
£25 and £31

B
£10 and £46

C
£20 and £36

D
£43 and £13

Solution

Let the amount received by Jeff be £x.

Then, amount received by Raghav = £(56 - x)

It is given that of one part is equal to of the other.
⇒ =(56 - x)
Dividing both sides by 2,

=(56 - x)
⇒ 9x = 5(56 - x)

⇒ 9x = 280 - 5x

⇒ 9x + 5x = 280

⇒ 14x = 280

⇒ x =
⇒ x = 20

Hence, the two parts are £20 and £(56 - 20) = £36.
Question 18
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Prateek is 48 years old. Shubham, his son, asks his father about his age, to which the father replies that after four years, he will be six years older than twice his age at that time. Find the present age of Shubham.

A
23 years

B
22 years

C
20 years

D
19 years

Solution

Prateek's present age = 48 years
Suppose, Shubham's present age is 'x' years.
Prateek's age after four years = 52 years
Shubham's age after four years = (x + 4) years
According to the question,
2(x + 4) + 6 = 52
2x + 8 + 6 = 52
2x = 52 - 14
2x = 38
x = 19
Question 19
1 / -0

While navigating a boat in a river, Akhil travels 60 km downstream. The speed of the boat in still water is 30 km/hr. He then comes back to the same place from where he started. Find the speed of the stream if it takes four and a half hours to complete the journey.

A
10 km/hr

B
20 km/hr

C
30 km/hr

D
40 km/hr

Solution

Let the speed of the stream be x km/hr.
Then,
Speed downstream = (30 + x) km/hr
Speed upstream = (30 – x) km/hr
Therefore, +=
=> =
=> 3600 × 2 = 9(900 - x²)
=> 7200 = 8100 - 9x²
=> 9x² = 8100 – 7200
=> 9x²= 900
=> x²= 100
=> x = 10
Question 20
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There are a total of 84 apples and oranges in a basket, of which of the apples and of the oranges are used for making jam. The total number of apples and oranges of the same basket which are used for making jam is 60. How many apples are there in the basket?

A
52

B
50

C
48

D
46

Solution

Let the number of apples in the basket be x.
Then, number of oranges in the basket = 84 – x
According to the question,
x + (84 – x) = 60

⇒ x - x + 56 = 60

⇒ x = 12 × 4
So, x = 48
The number of apples in the basket is 48.
Question 21
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Which of the following statements is/are CORRECT?

Statement (1): a = -1 is the solution of .

Statement (2): a = -5 is the solution of .

A
Only statement (1)

B
Only statement (2)

C
Both statement (1) and statement (2)

D
Neither statement (1) nor statement (2)

Solution

Statement (1):

Statement (2):

10a + 7 - 3a + 28 = 0

7a + 35 = 0

a =
a = -5

So, both statement (1) and statement (2) are correct.

Question 22

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Fill in the blanks with the help of the table given below.

(1) The solution of the equation is ________.
(2) The value of the variable which satisfies a given equation is called ________ of the equation.
(3) Any term of an equation may be taken to the other side with its sign changed. This process is called _________.

	(1)	(2)	(3)
P		solution	equation
Q		solution	transposition
R		equation	transposition
S		transposition	solution

Q

R

S

P

Solution

(1)

(2) The value of a variable which satisfies a given equation is called solution of the equation.

(3) Any term of an equation may be taken to the other side with its sign changed. This process is called transposition.

Question 23

1 / -0

Directions: Read the following statements and find which of them are true or false with the help of the table given below.

(P) Multiplying both sides of an equation by a non-zero constant will change its solution.
(Q) The perimeter of a rectangle is 180 cm. If the length of the rectangle is decreased by 4 cm and its breadth is increased by 4 cm, the area of the rectangle decreases by 88 sq. cm. The length and the breadth of the rectangle are 36 cm and 54 cm, respectively.
(R) The sum of two numbers is 1880. If 7.5% of one number is 12.5% of the other number, then one of the numbers will be 1175.

	P	Q	R
A	False	True	False
B	False	True	True
C	True	False	True
D	True	True	False

A

B

C

D

Solution

1. (P) is a false statement as multiplying both sides of an equation by a non-zero constant will not change its solution.
2. Let the length of the rectangle be x cm.
Perimeter = 180 cm
2(l + b) = 180
So, x + b = 90
b = (90 - x) cm
Area of the rectangle =

According to the question, we have

So,
Length = 36 cm
Breadth = 90 - 36 = 54 cm

3. Let one number be x.
Then, the other number will be 1880 - x.

On solving the above equation, we get

Question 24
1 / -0

Which of the following statements is INCORRECT?

(A) Raghu buys some t-shirts at the rate of Rs. 80 per t-shirt. He also buys an equal number of shirts at the rate of Rs. 100 per shirt. Then, he sells those t-shirts and shirts and makes a profit of 10% on t-shirts and 12% on shirts. At the end of the day, all t-shirts and shirts are sold out and his profit is Rs. 1240. Therefore, Raghu buys 62 t-shirts.
(B) A painter charges Rs. 7000 to paint the entire floor of the house. He works along with one labourer. The cost of materials used is Rs. 1800 and labour charges are Rs. 80 per hour. So, the painter will work for 65 hours.
(C) Rs. 280 is divided between x and y such that twice the y's share is less than x's share by Rs. 40. So, the y's share is Rs. 100.
(D) Aman thinks of a number and subtracts 5/2 from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. The number she thought of is 4.

A
(A)

B
(B)

C
(C)

D
(D)

Solution

(A) Let the number of t-shirts be x.
Number of shirts = x
Cost of x t-shirts = 80x
Cost of x shirts = 100x

According to the question,
10% of 80x + 12% of 100x = 1240

8x + 12x = 1240
20x = 1240
x = 62

(B) Suppose, the painter works for x hours.
So, labour charges for x hours = 80x
As per the information given in the question, we get
80x + 1800 = 7000
80x = 5200

x =

x = 65

(C) Let y's share be Rs. a.
Since 2 y's share + 40 = (x's share)
2a + 40 = (x's share)
According to the question,
a + 2a + 40 = 280
3a + 40 = 280
3a = 240
a = 80

(D) Let the number be x.

5x = 20
x = 4