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CBSE Questions for Class 8 Maths Linear Equations In One Variable Quiz 5 - MCQExams.com
CBSE
Class 8 Maths
Linear Equations In One Variable
Quiz 5
The sum of two consecutive odd natural numbers is
140
. Find the bigger number.
Report Question
0%
85
0%
71
0%
91
0%
69
Explanation
Let the integer be
x
.
The two consecutive odd number
=
x
,
x
+
2
Sum
=
x
+
x
+
2
=
140
2
x
=
138
x
=
69
The length of larger number
=
x
+
2
=
71
.
In a shooting competition a marksman receives
50
paise if he hits the mark and pays
20
paise if he misses it. He tried
60
shots and was paid Rs.
1.30
. How many times did he hit the mark?
Report Question
0%
10
0%
19
0%
14
0%
12
Explanation
Let the Number of hits be
x
Number of misses will be
60
−
x
Then according to the problem, we have
0.50
x
−
(
60
−
x
)
0.20
=
1.30
⇒
0.50
x
−
12.0
+
0.2
x
=
1.30
⇒
0.7
x
=
13.30
⇒
x
=
19
Number of times he hit the mark
=
19
.
Solve:
8
x
+
21
4
=
3
x
+
7
, then
x
=
Report Question
0%
2
9
0%
7
20
0%
6
17
0%
4
21
Explanation
Given,
8
x
+
21
4
=
3
x
+
7
Multiply
4
on both the sides, we get
32
x
+
21
=
12
x
+
28
Taking
x
to one side and constants to another side.
20
x
=
7
∴
x
=
7
20
Some part of a journey of
555
k
m
was completed by a car with speed
60
k
m
/
h
. Then the speed is increased by
15
k
m
/
h
and the journey is completed. If it takes
8
hours to reach, find the time taken by
60
k
m
/
h
speed.
Report Question
0%
11
0%
8
0%
13
0%
3
Explanation
Let time taken to cover some distance with
60
km/hr be
t
.
Then,
t
(
60
)
+
(
8
−
t
)
(
75
)
=
555
⇒
75
×
8
−
15
t
=
555
⇒
600
−
555
=
15
t
⇒
t
=
3
hours
Distance
=
3
×
60
=
180
km
Therefore, the time taken by
60
km/hr speed is
3
hours.
If
x
=
m
+
1
and
1
3
(
6
x
−
3
)
−
(
8
−
3
x
)
=
11
;
find the value of
m
.
Report Question
0%
m
=
7
0%
m
=
6
0%
m
=
2
0%
m
=
3
Explanation
Given,
1
3
(
6
x
−
3
)
−
(
8
−
3
x
)
=
11
As L.C.M. is
3
, we have
6
x
−
3
−
24
+
9
x
=
33
⇒
15
x
−
27
=
33
⇒
15
x
=
60
⇒
x
=
4
=
3
+
1
Thus comparing this with
x
=
m
+
1
, we get value of
m
as
3
.
The angles of a triangle are
2
(
x
−
7
)
,
3
2
(
x
−
1
)
and
3
(
x
+
11
)
. Find
x
and then show that the triangle is isosceles.
Report Question
0%
15
0%
18
0%
22
0%
25
Explanation
Sum of the angles
=
180
2
(
x
−
7
)
+
3
2
(
x
−
1
)
+
3
(
x
+
11
)
=
180
L
C
M
=
2
4
(
x
−
7
)
+
3
(
x
−
1
)
+
6
(
x
+
11
)
=
360
4
x
−
28
+
3
x
−
3
+
6
x
+
66
=
360
13
x
+
35
=
360
13
x
=
325
x
=
25
Angle
1
=
2
(
x
−
7
)
=
2
(
18
)
=
36
Angle
2
=
3
2
(
x
−
1
)
=
3
2
(
24
)
=
36
Since two angles are equal, it is an isosceles triangle.
The measures of the angles of a triangle are
2
x
,
x
+
25
and
3
x
+
5
. Find
x
and then show that the triangle is isosceles.
Report Question
0%
25
0%
15
0%
28
0%
12
Explanation
Measures of the angle
=
2
x
,
x
+
25
,
3
x
+
5
Sum of the angles
=
180
2
x
+
x
+
25
+
3
x
+
5
=
180
6
x
+
30
=
180
6
x
=
150
x
=
25
So, the angles of the triangle are
1)
2
x
=
50
2)
x
+
25
=
50
3)
3
x
+
5
=
80
Since two angles are equal, the triangle is isosceles.
The difference between
3
4
of a line and
2
5
of the same line is
28
cm. Find the length of the line.
Report Question
0%
39
cm
0%
45
cm
0%
80
cm
0%
40
cm
Explanation
Let the Length of the line is
x
.
Therefore,
3
4
x
−
2
5
x
=
28
⇒
7
x
20
=
28
⇒
7
x
=
20
×
28
⇒
x
=
80
Therefore, the length of a line is
80
cm.
A boy has
x
coins of
50
paise each
,
2
x
coins of
25
paise each,
4
x
coins of
10
paise each and
8
x
coins of
5
paise each. Find the number of
5
paise coins if the value of all the coins is Rs.
9
.
Report Question
0%
40
0%
20
0%
500
0%
300
Explanation
According to the problem, we have
x
(
0.50
)
+
2
x
(
0.25
)
+
4
x
(
0.10
)
+
8
x
(
0.05
)
=
9.00
⇒
0.5
x
+
0.5
x
+
0.4
x
+
0.4
x
=
9.0
⇒
1.8
x
=
9
⇒
x
=
5
Number of
5
paise coins
=
8
x
=
40
.
If
(
2
a
x
+
1
)
(
3
x
+
1
)
=
6
a
(
x
+
1
)
and
x
=
1
, find the value of
a
.
Report Question
0%
1
0%
4
0%
3
0%
2
Explanation
(
2
a
x
+
1
)
(
3
x
+
1
)
=
6
a
(
x
+
1
)
⟹
[
2
a
(
1
)
+
1
]
[
3
(
1
)
+
1
]
=
6
a
[
(
1
+
1
)
]
⟹
(
2
a
+
1
)
(
3
+
1
)
=
6
a
(
2
)
⟹
(
2
a
+
1
)
(
4
)
=
12
a
⟹
8
a
+
4
=
12
a
⟹
8
a
−
12
a
=
−
4
⟹
−
4
a
=
−
4
⟹
a
=
1
Two numbers are in the ratio
4
:
7
. If thrice the larger be added to twice the smaller, the sum is
59
. Find the numbers.
Report Question
0%
8
4
29
and
14
7
29
0%
8
3
34
and
14
7
5
0%
8
3
34
and
14
6
25
0%
8
4
29
and
14
2
19
Explanation
Let the numbers be
4
x
;
7
x
Given,
3
(
7
x
)
+
2
(
4
x
)
=
59
=>
21
x
+
8
x
=
59
29
x
=
59
=>
x
=
59
29
Thus the numbers are
4
x
=
4
×
59
29
=
236
29
=
8
4
29
and
7
x
=
7
×
59
29
=
413
29
=
14
7
29
In an examination, a student scores
4
marks for every correct answer and loses
1
mark for every wrong answer. If he attempts in all
60
questions and secures
130
marks, the number of questions he attempts correctly, is ___
Report Question
0%
35
0%
38
0%
40
0%
42
Explanation
Let the number of questions attempted correctly be
x
.
Then, number of incorrect ones
=
(
60
−
x
)
.
∴
4
x
−
1
(
60
−
x
)
=
130
⇒
5
x
=
190
⇒
x
=
38
So, number of questions student attempts correctly are
38
.
Amit is now
6
times as old as his son. Four years from now, the sum of their ages will be
43
years. Determine Amit's present age:
Report Question
0%
30
years
0%
32
years
0%
34
years
0%
28
years
Explanation
Let present age of Amit's son be
x
yrs and age of Amit be
6
x
yrs.
Four yrs from now,
(
6
x
+
4
)
+
(
x
+
4
)
=
43
.....(Given condition)
∴
7
x
=
35
∴
x
=
5
,
i.e., present age of Amit
=
6
x
=
6
×
5
=
30
yrs.
Hence, option
A
is the correct answer.
If
1
3
(
7
−
4
x
)
−
1
4
(
11
−
5
x
)
+
1
=
x
−
1
2
(
3
x
−
7
)
, then
x
=
Report Question
0%
1
0%
9
0%
6
0%
7
Explanation
1
3
(
7
−
4
x
)
−
1
4
(
11
−
5
x
)
+
1
=
x
−
1
2
(
3
x
−
7
)
L
C
M
=
12
4
(
7
−
4
x
)
−
3
(
11
−
5
x
)
+
12
=
12
x
−
6
(
3
x
−
7
)
28
−
16
x
−
33
+
15
x
+
12
=
12
x
−
18
x
+
42
7
−
x
=
42
−
6
x
5
x
=
35
x
=
7
The ten's digit of a two digit number exceeds its unit's digit by
4
. If the ten's digit and the unit's digit are in the ratio
3
:
1
, find the number.
Report Question
0%
62
0%
51
0%
65
0%
85
Explanation
Let the units digit
=
x
Let the tens digit
=
x
+
4
Tens digit : One digit ::
3
:
1
x
+
4
:
x
::
3
:
1
⇒
x
+
4
=
3
x
⇒
2
x
=
4
⇒
x
=
2
Tens digit
=
6
Therefore, the number is
62
.
Solve the following equation:
4
5
(
x
+
5
6
)
+
2
3
(
x
−
1
4
)
=
1
1
9
Report Question
0%
5
19
0%
5
16
0%
5
14
0%
5
12
Explanation
4
5
(
x
+
5
6
)
+
2
3
(
x
−
1
4
)
=
1
1
9
=>
4
x
5
+
20
30
+
2
x
3
−
2
12
=
10
9
=>
4
x
5
+
2
3
+
2
x
3
−
1
6
−
10
9
=
0
=>
72
x
+
60
+
60
x
−
15
−
100
90
=
0
=>
72
x
+
60
x
=
−
60
+
15
+
100
=>
132
x
=
55
=>
x
=
55
132
=>
x
=
5
12
A farmer divides his herd of
x
cows among his
4
sons so, that first son gets-one-half of the herd, the second son get, one-fourth, the third son gets one-fifth, and the fourth son gets
7
cows, then the value of
x
is :
Report Question
0%
100
0%
140
0%
160
0%
180
Explanation
Total number of cows
=
x
According to the question, we have
A
=
x
2
,
B
=
x
4
, C
=
x
5
,
D
=
7
∴
x
2
+
x
4
+
x
5
+
7
=
x
⇒
10
x
+
5
x
+
4
x
20
=
x
−
7
⇒
19
x
=
20
x
−
140
⇒
140
=
x
Hence, option 'B' is correct.
Out of six consecutive numbers the sum of first three is
27
. What is the sum of next three?
Report Question
0%
30
0%
40
0%
36
0%
45
Explanation
Let the first three consecutive numbers be
x
,
x
+
1
and
x
+
2
.
Then,
x
+
x
+
1
+
x
+
2
=
27
⇒
3
x
=
24
⇒
x
=
8
∴
The first three numbers are
8
,
9
,
10
.
⇒
The next three numbers are
11
,
12
,
13
.
Hence, the required sum
=
11
+
12
+
13
=
36
.
I bought a number of books one day, four times of them on the next day, and eight times on the third day, In all I bought
78
books. How many books did I buy on the second
day?
Report Question
0%
6
0%
8
0%
16
0%
24
0%
36
Explanation
Let the number of books bought of the first day be
a
Thus, number of books on second day
=
4
a
and the number of books on third day
=
8
a
Now, given
a
+
4
a
+
8
a
=
78
⇒
13
a
=
78
⇒
a
=
78
13
⇒
a
=
6
Thus, the number of books bought of second day
=
4
×
6
=
24
The difference of the squares of two consecutive even natural numbers isTaking x as the smaller of the two numbers, form an equation in x, and hence find the larger of the two numbers.
Report Question
0%
18
0%
24
0%
23
0%
21
Explanation
Given that,
The difference of squares of two consecutive even natural numbers is
92
.
The smaller number is
x
.
To find out,
(
i
)
The equation in
x
representing the given information.
(
i
i
)
The larger of the two numbers.
(
i
)
If the smaller number is
x
, then the larger number will be
x
+
2
According to the question,
(
x
+
2
)
2
−
x
2
=
92
Hence,
(
x
+
2
)
2
−
x
2
=
92
is the equation that represents the given information.
(
i
i
)
Solving
(
x
+
2
)
2
−
x
2
=
92
We know that,
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
Applying the same identity, we get:
(
x
2
+
4
x
+
4
)
−
x
2
=
92
⇒
x
2
+
4
x
+
4
−
x
2
=
92
⇒
4
x
+
4
=
92
Dividing both sides by
4
, we get:
x
+
1
=
23
x
=
23
−
1
=
22
Hence,
x
=
22
∴
x
+
2
=
22
+
2
=
24
Hence, the larger of the two numbers is
24
.
The difference between two numbers is
8
and their ratio is
1
:
5
. Which of the following is the smaller number?
Report Question
0%
24
0%
8
0%
10
0%
2
Explanation
Let the numbers be
x
and
5
x
.
Given,
5
x
−
x
=
8
⇒
4
x
=
8
⇒
x
=
8
4
=
2
Hence, smaller number is
2
.
The solution of the equation
3
a
−
2
3
+
2
a
+
3
2
=
a
+
7
6
is
Report Question
0%
a
=
2
0%
a
=
1
3
0%
a
=
−
2
0%
a
=
1
2
Explanation
Given,
3
a
−
2
3
+
2
a
+
3
2
=
a
+
7
6
L.C.M. of denominators is
6
.
Multiplying each term by
6
, we get
6
×
(
3
a
−
2
3
)
+
6
×
(
2
a
+
3
2
)
=
6
×
a
+
6
×
7
6
⇒
2
(
3
a
−
2
)
+
3
(
2
a
+
3
)
=
6
a
+
7
⇒
6
a
−
4
+
6
a
+
9
=
6
a
+
7
⇒
12
a
+
5
=
6
a
+
7
⇒
6
a
=
2
⇒
a
=
2
6
=
1
3
Hence, required solution is
a
=
1
3
.
The sum of one-half, one third and one-fourth of a number exceeds the number by
12
. What is the number?
Report Question
0%
72
0%
144
0%
98
0%
156
Explanation
Let the number be
x
.
Then,
(
x
2
+
x
3
+
x
4
)
−
x
=
12
,
L.C.M of
2
,
3
,
4
=
12
,
Thus multiplying above equation with
12
both sides,
⇒
12
×
x
2
+
12
×
x
3
+
12
×
x
4
−
12
×
x
−
12
×
12
⇒
6
x
+
4
x
+
3
x
−
12
x
=
144
⇒
13
x
−
12
x
=
144
⇒
x
=
144
.
Hence, the required number is
144.
Find the value of
y
in the equation :
(
2
−
3
y
)
+
4
y
9
y
−
(
8
y
+
7
)
=
4
5
Report Question
0%
18
0%
9
0%
−
38
0%
−
32
Explanation
Given,
(
2
−
3
y
)
+
4
y
9
y
−
(
8
y
+
7
)
=
4
5
⇒
2
+
y
y
−
7
=
4
5
⇒
5
(
2
+
y
)
=
4
(
y
−
7
)
....( cross multiplying )
⇒
10
+
5
y
=
4
y
−
28
⇒
y
=
−
38
Hence,. the solution is
y
=
−
38
Solve for
x
:
2
x
+
3
2
=
5
−
2
(
x
−
4
)
3
.
Report Question
0%
5
3
0%
12
29
0%
37
10
0%
None of these
Explanation
Given,
2
x
+
3
2
=
5
−
2
(
x
−
4
)
3
Multiplying all the terms by the LCM of
2
,
3
, i.e.,
6
, we get
6
×
(
2
x
+
3
)
2
=
6
×
5
−
6
×
2
(
x
−
4
)
3
⇒
3
(
2
x
+
3
)
=
30
−
4
(
x
−
4
)
⇒
6
x
+
9
=
30
−
4
x
+
16
⇒
6
x
+
9
=
−
4
x
+
46
⇒
6
x
+
4
x
=
46
−
9
⇒
10
x
=
37
⇒
x
=
37
10
Hence, required solution is
x
=
37
10
.
X buys pens and pencils at Rs. 5 and Rs. 1 per piece respectively. For every two pens, he buys three pencils. He sold pens and pencils at 12
%
and 10
%
profit respectively. If his total sale is Rs. 725, then the number of pencils exceeds the number of pens by
Report Question
0%
25
0%
50
0%
75
0%
90
Explanation
Let number of pens be
x
Hence, number of pencils will be
3
2
x
Cost of one pen is
R
s
.
5
Hence, total C.P. of pens
=
5
x
Also, cost of one pencil is
R
s
.
1
Hence, total C.P. of pencils
=
3
2
x
It is also given that, pens are sold at
12
%
profit,
Hence,
S
.
P
.
=
112
%
o
f
5
x
=
112
100
×
5
x
=
28
x
5
Also, pencils are sold at
10
%
profit,
Hence,
S
.
P
.
=
110
%
o
f
3
2
x
=
330
200
x
=
33
x
20
Now, total sale is
R
s
.
725
.
Hence,
28
x
5
+
33
x
20
=
725
112
x
+
33
x
=
725
×
20
145
x
=
14500
x
=
100
Thus, number of pens
=
100
Number of pencils
=
3
2
×
100
=
150
So, the number of pencils exceeds the number of pens by
50
.
Hence, option B is correct.
A candidate in an examination was asked to find
5
14
of a certain number. By mistake he found
5
4
of it. Thus his answer was
25
more than the correct answer. What was the number?
Report Question
0%
28
0%
56
0%
65
0%
20
Explanation
Let the number be x
Then
x
×
5
4
−
x
×
5
14
=
25
⇒
35
x
−
10
x
28
=
25
⇒
25
x
28
=
25
⇒
x
=
25
×
28
25
=
28
Solve for
x
:
3
x
4
−
(
x
−
1
)
3
=
(
x
−
2
)
2
.
Report Question
0%
9
0%
14
0%
16
0%
11
Explanation
Given,
3
x
4
−
(
x
−
1
)
3
=
(
x
−
2
)
2
L.C.M. of denominator
=
12
∴
Multiplying each term by
12
, we get
12
×
3
x
4
−
12
×
(
x
−
1
)
3
=
12
×
(
x
−
2
)
2
⇒
9
x
−
4
(
x
−
1
)
=
6
(
x
−
2
)
⇒
9
x
−
4
x
+
4
=
6
x
−
12
⇒
5
x
+
4
=
6
x
−
12
⇒
x
=
16
Hence, required value of
x
is
16
.
The solution of the the equation
5
(
3
x
+
5
)
=
2
(
7
x
−
4
)
is
Report Question
0%
x
=
17
0%
x
=
33
0%
x
=
−
33
0%
x
=
−
17
Explanation
Given,
5
(
3
x
+
5
)
=
2
(
7
x
−
4
)
∴
15
x
+
25
=
14
x
−
8
Putting
x
terms on one side and constants on another side.
∴
15
x
−
14
x
=
−
8
−
25
∴
x
=
−
33
Hence, option C is correct.
If two third, one half and one seventh of a number is added to itself the result is
37
. Find the number.
Report Question
0%
14
2
97
0%
16
2
97
0%
18
2
97
0%
None
Explanation
Let,
The number be
x
Two-third of a number
=
2
3
x
One-half of a number
=
1
2
x
One-seventh of a number
=
1
7
x
A.T.Q,
2
3
x
+
1
2
x
+
1
7
x
+
x
=
37
⟹
28
x
+
21
x
+
6
x
+
42
x
42
=
37
⟹
97
42
x
=
37
⟹
x
=
37
×
42
97
⟹
x
=
1554
97
=
16
2
97
Answer : B
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