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CBSE Questions for Class 8 Maths Linear Equations In One Variable Quiz 6 - MCQExams.com
CBSE
Class 8 Maths
Linear Equations In One Variable
Quiz 6
Two consecutive odd numbers are such that when the smaller number is subtracted from three times the bigger
number, the result is
56
. The bigger number is:
Report Question
0%
29
0%
31
0%
25
0%
27
Explanation
Let the two consecutive odd numbers are
x
and
x
+
2
.
Two consecutive odd numbers are such that when the smaller number is subtracted from three times the bigger
number, the result is
56
.
Hence, equation is,
3
(
x
+
2
)
−
x
=
56
∴
2
x
=
50
∴
x
=
25
∴
Smaller number is
25
and bigger number is
27
.
One number is 3 less than the two times of the other; if their sum is increased by 7 the result isFind the numbers.
Report Question
0%
9
,
11
0%
11
,
13
0%
11
,
19
0%
9
,
13
Explanation
Let one number = x
other number = 2x-3
(
x
+
2
x
−
3
)
+
7
=
37
3x = 33
x = 11
∴
The two number are 11 and 19
The total cost of three prizes is Rs.If the value of second prize is
3
4
th of the first and the value of 3rd prize is
1
2
of the second prize;
find the value of first prize.
Report Question
0%
Rs.
900
0%
Rs.
1500
0%
Rs.
1200
0%
Rs.
450
Explanation
Let First Prize be
x
Then Second Prize
=
3
4
x
Third Prize
=
1
2
×
3
x
4
=
3
x
8
x
+
3
x
4
+
3
x
8
=
2550
(given)
L.C.M of
1
,
4
,
8
is
8
.
x
×
8
1
×
8
+
3
x
×
2
4
×
2
+
3
x
8
=
2550
8
x
+
6
x
+
x
8
=
2550
17
x
8
=
2550
x
=
2550
×
8
17
x
=
R
s
.1200
∴
The value of first first prize is
R
s
.1200
If
7
x
+
2
6
−
x
−
4
3
=
x
+
3
3
, then
x
=
Report Question
0%
−
4
3
0%
1
3
0%
−
1
3
0%
1
1
3
Explanation
Given.
7
x
+
2
6
−
x
−
4
3
=
x
+
3
3
.
Multiply throughout by
3
, we get
∴
7
x
+
2
2
−
(
x
−
4
)
=
x
+
3
∴
7
x
+
2
2
=
2
x
−
1
On cross multiplying, we get
3
x
=
−
4
∴
x
=
−
4
3
The sum of 4 consecutive integers isThen the greatest among them is:
Report Question
0%
19
0%
23
0%
17
0%
16
Explanation
Let the
4
consecutive numbers be
x
,
x
+
1
,
x
+
2
,
x
+
3
Given: The sum of
4
consecutive numbers is
70
.
Therefore,
(
x
)
+
(
x
+
1
)
+
(
x
+
2
)
+
(
x
+
3
)
=
70
4
x
+
6
=
70
4
x
=
64
x
=
16
Therefore,
x
+
1
=
17
,
x
+
2
=
18
,
x
+
3
=
19
Thus the greatest is
19
Solve for
x
:
1
4
(
5
x
+
4
)
=
1
3
(
2
x
−
1
)
Report Question
0%
−
16
7
0%
10
7
0%
8
7
0%
−
15
7
Explanation
Given,
1
4
(
5
x
+
4
)
=
1
3
(
2
x
−
1
)
⇒
3
(
5
x
+
4
)
=
4
(
2
x
−
1
)
(
cross multiply
)
⇒
15
x
+
12
=
8
x
−
4
⇒
15
x
−
8
x
=
−
4
−
12
⇒
7
x
=
−
16
⇒
x
=
−
16
7
1
5
th of a flagpole is black and
1
4
th is white and the remaining three metres is painted yellow then ffind the length of the flagpole
Report Question
0%
5
5
11
m
0%
60
11
c
m
0%
5
k
m
0%
None
Explanation
Let the length of flagpole be
x
m
Length of flagpole which is black
=
1
5
x
m
Length of flagpole which is white
=
1
4
x
m
Length of flagpole which is yellow
=
3
m
A.T.Q,
1
5
x
+
1
4
x
+
3
=
x
⟹
x
−
x
5
−
x
4
=
3
⟹
20
x
−
4
x
−
5
x
20
=
3
⟹
11
x
=
3
×
20
⟹
x
=
60
11
⟹
x
=
5
5
11
m
∴
The length of flagpole
=
5
5
11
m
1
2
is subtracted from a number and the difference is multiplied by 4 , then 25 is added to the product and the sum is divided by 3 the result is equal toFind the number
Report Question
0%
3
5
0%
7
4
0%
6
7
0%
2
3
Explanation
Let the number be
x
Given
{
(
x
−
1
2
)
×
4
+
25
}
÷
3
=
10
{
4
x
−
2
+
25
}
×
1
3
=
10
(
4
x
+
23
3
)
=
10
4
x
+
23
=
30
4
x
=
7
⇒
x
=
7
4
In a piggy bank, the number of
25
paise coins are five times the number of
50
paise coins. If there are
120
coins find the amount in the bank ?
Report Question
0%
Rs.
25
0%
Rs.
10
0%
Rs.
35
0%
Rs.
40
Explanation
Let number of
50
paise coins
=
x
then number of
25
paise coins
=
5
x
Given total number of coins
=
120
⇒
x
+
5
x
=
120
⇒
6
x
=
120
⇒
x
=
120
6
=
20
∴
Number of
50
paise coins
=
20
Thus Amount
20
×
50
=
Rs.
10
And number of
25
paise coins
=
5
×
20
=
100
Thus amount
=
25
×
100
=
Rs.
25
Hence, total amount
25
+
10
=
Rs.
35
.
Rina is
x
years old. Her sister Bina is
5
years older than her. If their ages add up to
15
, then Bina's age is
Report Question
0%
a multiple of
5
0%
a multiple of
6
0%
a multiple of
7
0%
divisible by
8
Explanation
Age of Rina
=
x
Age of Bina
=
(
x
+
5
)
Sum of their ages
=
x
+
x
+
5
According to the statement:
2
x
+
5
=
15
2
x
=
10
x
=
5
Hence, option A is correct.
Divide 224 into three parts so that the second will be twice the first and third will be twice the second
Report Question
0%
26
,
52
,
104
0%
24
,
48
,
96
0%
18
,
36
,
72
0%
32
,
64
,
128
Explanation
Let the first part be
x
Then, second part
=
2
x
Third Part
=
2
×
2
x
=
4
x
Given,
x
+
2
x
+
4
x
=
224
⇒
x
=
224
7
=
32
∴
The three parts are
32
,
2
×
32
,
4
×
32
i.e.
32
,
64
,
128
.
Ages of two friends are in the ratio
2
:
1
. If sum of their ages is
51
then their ages are
Report Question
0%
34
yrs,
20
yrs
0%
34
yrs,
17
yrs
0%
20
yrs,
10
yrs
0%
30
yrs,
15
yrs
Explanation
Given ages in the ratio
2
:
1
Thus let their ages be
2
x
and
x
Given, the sum of their ages is
51
Therefore,
2
x
+
x
=
51
⇒
3
x
=
51
⇒
x
=
17
Hence, required age's are
34
yrs and
17
yrs.
Solve:
6
x
−
1
=
2
x
+
9
Report Question
0%
1
1
2
0%
−
2
1
2
0%
4
10
0%
2
1
2
Explanation
Given,
6
x
−
1
=
2
x
+
9
Bringing all
x
terms to one side and constants to another side.
6
x
−
2
x
=
9
+
1
⇒
4
x
=
10
⇒
x
=
10
4
=
5
2
=
2
1
2
Hence, solution is
x
=
2
1
2
.
In a two digit number the digit at the unit's place is four times the digit in the ten's place and the sum of the digits is equal to 10 What is the number?
Report Question
0%
14
0%
44
0%
82
0%
28
Explanation
Let the digit at ten's place
=
x
Then digit at unit's place
=
4
x
Sum of digit
=
10
⇒
x
+
4
x
=
10
⇒
5
x
=
10
⇒
x
=
2
∴
The number
=
10
×
x
+
4
x
=
10
×
2
+
4
×
2
=
20
+
8
=
28
If the sum of one-half and one-fifth of a number exceeds one-third of that number by
7
1
3
then the number is
Report Question
0%
15
0%
18
0%
20
0%
30
Explanation
Let the number be
x
Given
(
x
2
+
x
5
)
−
x
3
=
7
1
3
=
22
3
⇒
15
x
+
6
x
−
10
x
30
=
22
3
⇒
11
x
30
=
22
3
⇒
x
=
220
11
=
20
A train starts with full of passengers. At the first station, the train drops one-third of the passengers and takes in 96 more. At the next station one-half of the passengers on board get down while 12 new passengers get on board If the passengers on board now are 240 the number of passengers in the beginning was
Report Question
0%
540
0%
600
0%
444
0%
430
Explanation
Let the full number of passengers be
x
Number of passengers at the first station , after drops one-third of the passenger
=
(
x
−
1
3
x
)
+
96
=
2
x
3
+
96
Number of passengers at the second station , after one-half get down and 12 added
=
1
2
(
2
x
3
+
96
)
+
12
=
x
3
+
48
+
12
=
x
3
+
60
Given
x
3
+
60
=
240
⇒
x
3
=
240
−
60
=
180
⇒
x
=
180
×
3
=
540
Rs
770
have to be divided among A, B and C such that A receives 2/9th of what B and C together receive. Then A's share is
Report Question
0%
Rs
140
0%
Rs
154
0%
Rs
165
0%
Rs
170
Explanation
Let, B and C together receives
R
s
.
x
∴
A's share
=
2
9
x
A.T.Q,
x
+
2
9
x
=
770
⟹
9
x
+
2
x
9
=
770
⟹
11
x
=
770
×
9
⟹
x
=
770
×
9
11
=
630
A's Share
=
2
9
×
630
=
140
A sum of Rs 36.90 is made up of 180 coins which are either 10 paise coins or 25 paise coins Determine the number of each type of coins
Report Question
0%
126
of
10
p coins and
54
of
25
p coins
0%
54
of
10
p coins and
126
of
25
p coins
0%
90
of
10
p coins and
90
of
25
p coins
0%
54
of
10
p coins and
90
of
25
p coins
Explanation
Given : Total no of coins
=
180
Let, the no of
10
paise coins
x
No of
25
paise coins
=
180
−
x
Value of
10
paise coins
=
10
x
Value of
25
paise coins
=
25
(
180
−
x
)
A.T.Q,
10
x
+
25
(
180
−
x
)
=
3690
⟹
10
x
+
4500
−
25
x
=
3690
⟹
4500
−
3690
=
25
x
−
10
x
⟹
15
x
=
810
⟹
x
=
810
15
=
54
∴
No of
10
paise coins
=
54
No of
25
paise coins
=
180
−
54
=
126
If the sum of four consecutive odd numbers is
40
, then the smallest number is
Report Question
0%
7
0%
9
0%
11
0%
13
Explanation
Let the first odd number be
x
.
Thus, the other consecutive numbers are
x
+
2
,
x
+
4
,
x
+
6
Now, given that sum of all four numbers is 40,
x
+
x
+
2
+
x
+
4
+
x
+
6
=
40
⇒
4
x
+
12
=
40
⇒
4
x
=
28
⇒
x
=
7
Thus, the smallest number
7
.
If
50
is subtracted from two-third of a number, the result is equal to sum of
40
and one-fourth of that number. What is the number?
Report Question
0%
256
0%
216
0%
186
0%
144
Explanation
Let the number be
x
.
According to the statement,
2
x
3
−
50
=
x
4
+
40
2
x
3
−
x
4
=
50
+
40
8
x
−
3
x
12
=
90
5
x
12
=
90
x
=
90
×
12
5
=
216
Out of three numbers, the first is twice the second and the second is thrice the third. If the average of the three numbers is
10
,
find the largest number?
Report Question
0%
18
0%
14
0%
22
0%
24
Explanation
Let the third number be
x
.
Then, second number
=
3
x
and first number
=
6
x
Given,
x
+
3
x
+
6
x
3
=
10
⇒
10
x
=
30
⇒
x
=
3
∴
Largest number
=
6
x
=
6
×
3
=
18
In a zoo there are rabbits and pigeons. If their heads are counted these are 90 while their legs are 224 The number of pigeons in the zoo are
Report Question
0%
70
0%
68
0%
72
0%
22
Explanation
Let the number of rabbits be
x
No of heads
=
90
⇒
No of pigeons
=
(
90
−
x
)
Since a pigeon has
2
legs and a rabbit has 4 legs
x
×
4
+
(
90
−
x
)
×
2
=
224
⇒
4
x
+
180
−
2
x
=
224
⇒
2
x
=
224
−
180
=
44
⇒
x
=
22
∴
No of pigeons
=
90
−
22
=
68
Dhruv earned some money. He spent
1
3
of the money on magazines and
1
4
of the money on a snack. Which of the following fractions represents the part of money he did not spend?
Report Question
0%
5
12
0%
1
2
0%
2
3
0%
5
7
Explanation
Let the money earned by Dhruv be
x
.
Then, money on magazines is
1
3
x
, and money spent on snack is
1
4
x
.
So, money not spent is clearly,
x
−
x
3
−
x
4
=
5
x
12
.
Hence, option A is correct.
The sum of the digits of a three-digit number is
16
. If the ten's digit of the number is
3
times the unit's digit and the unit's digit is one-fourth of the hundredth digit then what is the number?
Report Question
0%
446
0%
561
0%
682
0%
862
Explanation
Let the hundredth's digit of the number be
x
Then unit's digit
=
x
4
and ten's digit
=
3
x
4
Given,
The sum of the digits is
16
⇒
x
+
x
4
+
3
x
4
=
16
⇒
4
x
+
x
+
3
x
4
=
16
⇒
2
x
=
16
⇒
x
=
8
ten's digit
=
3
x
4
=
3
×
8
4
=
6
unit's digit
=
x
4
=
8
4
=
2
∴
Required number
=
100
×
8
+
10
×
6
+
2
=
800
+
60
+
2
=
862
The required number is
862
The ratio of a two digit number to the sum of its digits is
7
:
1.
If the digit in the ten's place is
1
more than the digit in the one's place, then the number is
Report Question
0%
65
0%
43
0%
32
0%
21
Explanation
Let the digit at the unit's place in a
2
digit number be
x
.
Then, the digit at the ten's place
=
x
+
1
.
∴
The number
=
10
(
x
+
1
)
+
x
=
11
x
+
10
Sum of digits
=
x
+
1
+
x
=
2
x
+
1
Given,
11
x
+
10
2
x
+
1
=
7
1
11
x
+
10
=
14
x
+
7
3
x
=
3
⇒
x
=
1
∴
The number
=
11
×
1
+
10
=
21
Given that
−
6
p
−
9
3
=
2
p
+
9
5
, find the value of
p
.
Report Question
0%
−
4
0%
−
2
0%
3
0%
5
Explanation
Given,
−
6
p
−
9
3
=
2
p
+
9
5
⇒
−
2
p
−
3
=
2
p
+
9
5
⇒
−
10
p
−
15
=
2
p
+
9
⇒
−
12
p
=
24
⇒
p
=
−
2
If
2
x
+
3
=
x
−
4
,
then the value of
x
is
Report Question
0%
−
4
0%
−
7
0%
−
9
0%
−
10
Explanation
Step -1: Solve linnear equation in variable with variable on both sides.
Given
2
x
+
3
=
x
−
4
put x terms on one side and constants on another side.
⇒
2
x
−
x
=
−
4
−
3
⇒
x
=
−
7
Hence, the value of x is -7.
Hence , option B is correct. The value of x is -7.
If the sum of three consecutive even numbers is
234
, then the smallest among them is
Report Question
0%
76
0%
78
0%
80
0%
None of these
Explanation
Let the three consecutive even numbers be
2
x
−
2
,
2
x
,
2
x
+
2
.
We have,
(
2
x
−
2
)
+
2
x
+
(
2
x
+
2
)
=
234
⇒
6
x
=
234
⇒
x
=
39
∴
Least even number is
2
x
−
2
=
2
(
39
)
−
2
=
76
.
2
n
is an even number. What are the odd numbers on each side of it? The sum of two consecutive odd numbers is
96
. What are they?
Report Question
0%
41
,
43
0%
57
,
59
0%
47
,
49
0%
31
,
33
Explanation
Given: Even number
=
2
n
The odd number preceding
2
n
=
2
n
−
1
The odd number succeeding
2
n
=
2
n
+
1
A.T.Q,
2
n
−
1
+
2
n
+
1
=
96
⟹
4
n
=
96
⟹
n
=
96
4
=
24
∴
the consecutive odd numbers are
2
×
24
−
1
=
47
and
2
×
47
+
1
=
49
They are
47
,
49
3
x
=
2
x
+
20
What is the value of the
x
?
Report Question
0%
16
0%
18
0%
20
0%
22
Explanation
We have,
3
x
=
2
x
+
20
⇒
3
x
−
2
x
=
20
[Transposing
2
x
to LHS]
⇒
x
=
20
0:0:1
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Answered
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