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CBSE Questions for Class 12 Commerce Applied Mathematics Linear Equations Quiz 5 - MCQExams.com
CBSE
Class 12 Commerce Applied Mathematics
Linear Equations
Quiz 5
Solve the following equations by substitution method.
3
y
−
2
x
=
9
;
2
x
+
5
y
=
15
Report Question
0%
x
=
0
,
y
=
2
0%
x
=
5
,
y
=
2
0%
x
=
1
,
y
=
3
0%
x
=
0
,
y
=
3
Explanation
3
y
−
2
x
=
9
;
2
x
+
5
y
=
15
y
=
9
+
2
x
3
Put it in second equation.
2
x
+
5
×
9
+
2
x
3
=
15
6
x
+
45
+
10
x
=
45
16
x
=
0
x
=
0
y
=
9
+
2
x
3
=
9
+
2
(
0
)
3
=
3
y
=
3
Solve the following equations by substitution method.
x
=
2
y
−
1
;
y
=
2
x
−
7
Report Question
0%
x
=
8
,
y
=
3
0%
x
=
2
,
y
=
3
0%
x
=
5
,
y
=
3
0%
x
=
1
,
y
=
3
Explanation
x
=
2
y
−
1
;
y
=
2
x
−
7
x
=
2
y
−
1
Put it in second equation.
y
=
2
×
(
2
y
−
1
)
−
7
y
=
4
y
−
9
y
=
3
and
x
=
2
y
−
1
=
2
×
3
−
1
=
5
x
=
5
x
=
5
a
n
d
y
=
3
Solve the following equations by substitution method.
3
a
−
2
b
=
−
10
;
2
a
+
3
b
=
2
Report Question
0%
a
=
−
2
,
b
=
2
0%
a
=
−
1
,
b
=
2
0%
a
=
−
4
,
b
=
2
0%
a
=
−
7
,
b
=
2
Explanation
3
a
−
2
b
=
−
10
;
2
a
+
3
b
=
2
a
=
2
b
−
10
3
⇒
Put it in second equation.
2
×
2
b
−
10
3
+
3
b
=
2
4
b
−
20
+
9
b
=
6
13
b
=
26
∴
b
=
2
a
=
2
b
−
10
3
=
2
(
2
)
−
10
3
=
−
2
a
=
−
2
and
b
=
2
Solve the following simultaneous equations by the method of equating coefficients.
5
x
+
7
y
=
17
;
7
x
+
5
y
=
19
Report Question
0%
x
=
1
,
y
=
1
0%
x
=
4
,
y
=
1
0%
x
=
3
,
y
=
1
0%
x
=
2
,
y
=
1
Explanation
5
x
+
7
y
=
17
...(i)
7
x
+
5
y
=
19
...(ii)
On multiplying (i) by 7 and (ii) by 5, we get
35
x
+
49
y
=
119
3
−
5
x
+
−
25
y
=
9
−
5
_
24
y
=
24
∴
y
=
1
On putting
y
=
1
in (i), we get
5
x
+
7
(
1
)
=
17
⇒
x
=
2
∴
x
=
2
,
y
=
1
Solve the following equations by substitution method.
5
x
+
3
y
=
21
;
2
x
−
y
=
4
Report Question
0%
x
=
3
,
y
=
2
0%
x
=
−
3
,
y
=
2
0%
x
=
3
,
y
=
−
2
0%
None of these
Explanation
5
x
+
3
y
=
21
.........(1)
2
x
−
y
=
4
...............(2)
y
=
2
x
−
4
5
x
+
3
(
2
x
−
4
)
=
21
.........putting value of
y
in (1)
⇒
5
x
+
6
x
−
12
=
21
⇒
11
x
=
33
.......................
x
=
3
Putting value of
x
in (2)
6
−
y
=
4
..........................
y
=
2
Solve the following simultaneous equations by the method of equating coefficients.
x
3
+
5
y
=
13
;
2
x
+
y
2
=
19
Report Question
0%
x
=
1
,
y
=
2
0%
x
=
9
,
y
=
2
0%
x
=
4
,
y
=
2
0%
x
=
8
,
y
=
2
Explanation
x
3
+
5
y
=
13
....(i)
2
x
+
y
2
=
19
.....(ii)
Multiplying equation (i) by
3
and equation (ii) by
2
. we get,
x
+
15
y
=
39
......(iii)
4
x
+
y
=
38
......(iv)
T
o make the coefficients of
x equal m
ultiplying equation (iii) by
4
. we get ,
4
x
+
60
y
=
156
.....(v)
Subtract equation (iii) from equation (iv). we get,
4
x
+
60
y
−
(
4
x
+
y
)
=
156
−
38
59
y
=
118
⇒
y
=
2
Substitute
y
=
2
in equation (iii). we get,
x
+
15
(
2
)
=
39
⇒
x
=
9
∴
x
=
9
,
y
=
2
Solve the following simultaneous equations by the method of equating coefficients.
x
−
2
y
=
−
10
;
3
x
−
5
y
=
−
12
Report Question
0%
x
=
16
,
y
=
18
0%
x
=
32
,
y
=
18
0%
x
=
26
,
y
=
18
0%
x
=
22
,
y
=
18
Explanation
x
−
2
y
=
−
10
...(i)
3
x
−
5
y
=
−
12
...(ii)
On multiplying (i) by 3, we get
3
x
−
6
y
=
−
30
...(iii)
now subtracting (ii) from (iii)
3
x
−
6
y
=
−
30
3
−
x
−
+
5
y
=
−
+
12
_
−
y
=
−
18
∴
y
=
18
On putting
y
=
18
in (ii), we get
3
x
−
5
(
18
)
=
−
12
3
x
−
90
=
−
12
3
x
=
78
x
=
26
∴
x
=
26
,
y
=
18
Find the values of
(
x
+
y
)
and
(
x
−
y
)
without actually solving for
x
and
y
.
8
x
−
7
y
=
11
;
7
x
−
8
y
=
4
Report Question
0%
x
+
y
=
2
,
x
−
y
=
1
0%
x
+
y
=
1
,
x
−
y
=
1
0%
x
+
y
=
7
,
x
−
y
=
1
0%
x
+
y
=
3
,
x
−
y
=
1
Explanation
Rewriting the given equations, we get
8
x
−
7
y
=
11
...(i)
7
x
−
8
y
=
4
...(ii)
On adding (i) and (ii) , we get
15
x
−
15
y
=
15
⇒
x
−
y
=
1
On subtracting (ii) from (i), we get
x
+
y
=
7
Find the values of
(
x
+
y
)
and
(
x
−
y
)
without actually solving for
x
and
y
.
13
x
+
15
y
=
114
a
n
d
15
x
+
13
y
=
110
Report Question
0%
x
+
y
=
9
,
x
−
y
=
−
2
0%
x
+
y
=
8
,
x
−
y
=
−
2
0%
x
+
y
=
3
,
x
−
y
=
−
2
0%
x
+
y
=
1
,
x
−
y
=
−
2
Explanation
13
x
+
15
y
=
114
...(i)
15
x
+
13
y
=
110
...(ii)
On adding (i) and (ii) , we get
28
x
+
28
y
=
224
⇒
x
+
y
=
224
28
=
8
On subtracting (i) from (ii) , we get
2
x
−
2
y
=
−
4
⇒
x
−
y
=
−
4
2
=
−
2
.
Find the values of
(
x
+
y
)
and
(
x
−
y
)
without actually solving for
x
and
y
.
15
x
−
12
y
=
69
;
12
x
−
15
y
=
39
Report Question
0%
x
+
y
=
10
,
x
−
y
=
4
0%
x
+
y
=
5
,
x
−
y
=
4
0%
x
+
y
=
13
,
x
−
y
=
4
0%
x
+
y
=
19
,
x
−
y
=
4
Explanation
15
x
−
12
y
=
69
...(i)
12
x
−
15
y
=
39
...(ii)
On adding (i) and (ii) , we get
27
x
−
27
y
=
108
⇒
x
−
y
=
4
On subtracting (ii) from (i) , we get
3
x
+
3
y
=
30
⇒
x
+
y
=
10
Find the values of
(
x
+
y
)
and
(
x
−
y
)
without actually solving for
x
and
y
.
9
x
+
11
y
=
78
;
11
x
+
9
y
=
82
Report Question
0%
x
+
y
=
2
,
x
−
y
=
2
0%
x
+
y
=
8
,
x
−
y
=
2
0%
x
+
y
=
7
,
x
−
y
=
2
0%
x
+
y
=
3
,
x
−
y
=
2
Explanation
9
x
+
11
y
=
78
...(i)
11
x
+
9
y
=
82
...(ii)
On adding (i) and (ii) , we get
20
x
+
20
y
=
160
⇒
x
+
y
=
8
On subtracting (i) from (ii) , we get
2
x
−
2
y
=
4
⇒
x
−
y
=
2
Solve the following simultaneous equations by the method of equating coefficients.
4
x
+
y
=
34
;
x
+
4
y
=
16
Report Question
0%
x
=
8
,
y
=
2
0%
x
=
4
,
y
=
2
0%
x
=
9
,
y
=
2
0%
x
=
2
,
y
=
2
Explanation
4
x
+
y
=
34
...(i)
x
+
4
y
=
16
...(ii)
On multiplying (ii) by 4, we get
4
x
+
16
y
=
64
...(iii)
now subtracting (i) from (iii)
4
x
+
16
y
=
64
4
−
x
+
−
y
=
3
−
4
_
15
y
=
30
∴
y
=
2
On putting
y
=
2
in (i), we get
4
x
+
2
=
34
x
=
8
∴
x
=
8
,
y
=
2
Solve the following simultaneous equations by the method of equating coefficients.
2
x
−
y
3
+
3
x
−
2
y
=
3
;
4
x
−
3
y
+
5
x
−
4
y
4
=
1
Report Question
0%
x
=
4
,
y
=
5
0%
x
=
3
,
y
=
5
0%
x
=
7
,
y
=
5
0%
x
=
9
,
y
=
5
Explanation
2
x
−
y
3
+
3
x
−
2
y
=
3
....(i)
4
x
−
3
y
+
5
x
−
4
y
4
=
1
.....(ii)
Multiplying equation (i) by
3
and equation (ii) by
4
. we get,
2
x
−
y
+
9
x
−
6
y
=
9
⇒
11
x
−
7
y
=
9
.......(iii)
16
x
−
12
y
+
5
x
−
4
y
=
4
⇒
21
x
−
16
y
=
4
....(iv)
Multiplying equation (iii) by
16
and equation (iv) by
7
. we get,
176
x
−
112
y
=
144
1
−
47
x
−
+
112
y
=
2
−
8
_
29
x
=
116
⇒
x
=
4
Substitute
x
=
4
in equation (iii). we get,
11
(
4
)
−
7
y
=
9
⇒
7
y
=
35
⇒
y
=
5
∴
x
=
4
,
y
=
5
Solve for
x
and
y
.
5
x
+
6
y
=
7
x
+
3
y
=
3
(
x
+
6
y
−
6
)
Report Question
0%
x
=
1
,
y
=
3
0%
x
=
2
,
y
=
6
0%
x
=
3
,
y
=
2
0%
None of these
Explanation
Given,
5
x
+
6
y
=
7
x
+
3
y
=
3
(
x
+
6
y
−
6
)
By taking first and third we get,
5
x
+
6
y
=
3
(
x
+
6
y
−
6
)
⇒
5
x
+
6
y
=
3
x
+
18
y
−
18
⇒
2
x
−
12
y
=
−
18
....(i)
By taking last two we get,
7
x
+
3
y
=
3
(
x
+
6
y
−
6
)
7
x
+
3
y
=
3
x
+
18
y
−
18
⇒
4
x
−
15
y
=
−
18
.....(ii)
On multiplying equation (i) by
2
. we get,
4
x
−
24
y
=
−
36
....(iii)
Subtracting (ii) from (iii). we get,
4
x
−
24
y
−
(
4
x
−
15
y
)
=
−
36
−
(
−
18
)
∴
−
9
y
=
−
18
⇒
y
=
2
On substituting
y
=
2
in (i). we get,
2
x
−
12
(
2
)
=
−
18
⇒
2
x
=
6
∴
x
=
3
∴
x
=
3
,
y
=
2
Solve the following simultaneous equations:
x
3
+
y
4
=
4
;
5
x
6
−
y
8
=
4
Report Question
0%
x
=
5
,
y
=
8
0%
x
=
2
,
y
=
8
0%
x
=
1
,
y
=
8
0%
x
=
6
,
y
=
8
Explanation
x
3
+
y
4
=
4
⇒
4
x
+
3
y
=
48
....(i)
5
x
6
−
y
8
=
4
⇒
20
x
−
3
y
=
96
....(ii)
Since, coefficients of
y
are equal in both equations but with opposite sign.
So on adding (i) and (ii). we get,
4
x
+
3
y
+
20
x
−
3
y
=
48
+
96
⇒
24
x
=
144
⇒
x
=
6
On substituting
x
=
6
in (i). we get,
4
(
6
)
+
3
y
=
48
⇒
3
y
=
24
⇒
y
=
8
∴
x
=
6
,
y
=
8
Solve the following simultaneous equation.
12
x
+
17
y
=
53
;
17
x
+
12
y
=
63
Report Question
0%
x
=
3
,
y
=
1
0%
x
=
2
,
y
=
1
0%
x
=
1
,
y
=
1
0%
x
=
9
,
y
=
1
Explanation
12
x
+
17
y
=
53
...(i)
17
x
+
12
y
=
63
...(ii)
On adding (i) and (ii) , we get
29
x
+
29
y
=
116
⇒
x
+
y
=
4
....(iii)
On subtracting (i) from (ii) , we get
5
x
−
5
y
=
10
⇒
x
−
y
=
2
....(iv)
On adding (iii) and (iv) , we get
2
x
=
6
⇒
x
=
3
By putting
x
=
3
in (iii), we get
3
+
y
=
4
⇒
y
=
1
Solve the following pair of equations
64
p
−
45
q
=
289
;
45
p
−
64
q
=
365
Report Question
0%
p
=
0
,
q
=
−
5
0%
p
=
4
,
q
=
−
5
0%
p
=
1
,
q
=
−
5
0%
p
=
2
,
q
=
−
5
Explanation
Solution:
64
p
−
45
q
=
289
.............(1)
45
p
−
64
q
=
365
.............(2)
Adding equation (1) and (2) we get,
109
p
−
109
q
=
654
i.e.,
p
−
q
=
6
.........(3)
Subtracting equation (1) and (2) we get,
19
p
+
19
q
=
−
76
i.e.,
p
+
q
=
−
4
.........(4)
Adding equation (3) and (4) we get,
p
=
1
and substituting
p
=
1
in equation (3) we get,
q
=
−
5
Solve the following pair of equations
31
x
−
42
y
=
51
;
42
x
−
31
y
=
95
Report Question
0%
x
=
3
,
y
=
1
0%
x
=
2
,
y
=
1
0%
x
=
1
,
y
=
1
0%
x
=
6
,
y
=
1
Explanation
31
x
−
42
y
=
51
...(i)
42
x
−
31
y
=
95
...(ii)
On adding (i) and (ii) , we get
73
x
−
73
y
=
146
⇒
x
−
y
=
2
....(iii)
On subtracting (i) from (ii) , we get
11
x
+
11
y
=
44
⇒
x
+
y
=
4
....(iv)
On adding (iii) and (iv) , we get
2
x
=
6
⇒
x
=
3
By putting
x
=
3
in (iv), we get
3
+
y
=
4
⇒
y
=
1
∴
x
=
3
,
y
=
1
From the following figure, we can say:
x
3
+
y
4
=
4
;
5
x
6
−
y
8
=
4
Report Question
0%
x
=
1
,
y
=
8
0%
x
=
7
,
y
=
8
0%
x
=
6
,
y
=
8
0%
x
=
3
,
y
=
8
Explanation
Given ,
x
3
+
y
4
=
4
;
5
x
6
−
y
8
=
4
Rewriting the given equations, we get
4
x
+
3
y
=
48
...(i)
20
x
−
3
y
=
96
...(ii)
On adding (i) and (ii), we get
24
x
=
144
⇒
x
=
6
On putting
x
=
6
in (i), we get
4
(
6
)
+
3
y
=
48
⇒
y
=
8
∴
x
=
6
,
y
=
8
Solve the following pair of equations
2
x
15
+
y
5
=
4
;
x
3
=
y
2
Report Question
0%
x
=
15
,
y
=
10
0%
x
=
20
,
y
=
10
0%
x
=
5
,
y
=
10
0%
x
=
13
,
y
=
10
Explanation
Given,
2
x
15
+
y
5
=
4
;
x
3
=
y
2
Rewriting the given equations, we get
2
x
+
3
y
=
60
...(i)
2
x
−
3
y
=
0
...(ii)
On adding (i) and (ii) , we get
4
x
=
60
⇒
x
=
15
On putting
x
=
15
in (i), we get
2
(
15
)
+
3
y
=
60
⇒
y
=
10
∴
x
=
15
,
y
=
10
Solve the following pair of equations.
35
x
−
37
y
=
68
;
35
y
−
37
x
+
76
=
0
Report Question
0%
x
=
2
,
y
=
1
0%
x
=
3
,
y
=
1
0%
x
=
6
,
y
=
1
0%
x
=
1
,
y
=
1
Explanation
Rewriting the given equations, we get
35
x
−
37
y
=
68
...(i)
−
37
x
+
35
y
=
−
76
⇒
37
x
−
35
y
=
76
...(ii)
On adding (i) and (ii) , we get
72
x
−
72
y
=
144
⇒
x
−
y
=
2
....(iii)
On subtracting (i) from (ii) , we get
2
x
+
2
y
=
8
⇒
x
+
y
=
4
....(iv)
On adding (iii) and (iv) , we get
2
x
=
6
⇒
x
=
3
By putting
x
=
3
in (iv), we get
3
+
y
=
4
⇒
y
=
1
Find the values of
(
m
+
n
)
and
(
m
−
n
)
without actually solving for
m
and
n
.
17
m
+
13
n
=
133
;
13
m
+
17
n
=
137
Report Question
0%
m
+
n
=
5
,
m
−
n
=
−
1
0%
m
+
n
=
1
,
m
−
n
=
−
1
0%
m
+
n
=
2
,
m
−
n
=
−
1
0%
m
+
n
=
9
,
m
−
n
=
−
1
Explanation
17
m
+
13
n
=
133
...(i)
13
m
+
17
n
=
137
...(ii)
On adding (i) and (ii) , we get
30
m
+
30
n
=
270
⇒
m
+
n
=
9
On subtracting (ii) from (i) , we get
4
m
−
4
n
=
−
4
⇒
m
−
n
=
−
1
Solve the following pair of equations.
4
(
x
+
2
)
+
5
(
y
+
2
)
=
20
and
5
x
+
4
y
=
7
Report Question
0%
x
=
7
,
y
=
−
2
0%
x
=
4
,
y
=
−
2
0%
x
=
3
,
y
=
−
2
0%
x
=
2
,
y
=
−
2
Explanation
4
(
x
+
2
)
+
5
(
y
+
2
)
=
20
⇒
4
x
+
5
y
=
2
....(i)
5
x
+
4
y
=
7
........(ii)
On adding (i) and (ii) , we get
9
x
+
9
y
=
9
⇒
x
+
y
=
1
....(iii)
On subtracting (i) from (ii) , we get
x
−
y
=
5
....(iv)
On adding (iii) and (iv) , we get
2
x
=
6
⇒
x
=
3
By putting
x
=
3
in (iv), we get
3
−
y
=
5
⇒
y
=
−
2
∴
x
=
3
,
y
=
−
2
Solve the following pair of equations.
25
x
−
24
y
=
197
;
24
x
−
25
y
=
195
Report Question
0%
x
=
1
,
y
=
−
3
0%
x
=
9
,
y
=
−
3
0%
x
=
5
,
y
=
−
3
0%
x
=
3
,
y
=
−
3
Explanation
25
x
−
24
y
=
197
...(i)
24
x
−
25
y
=
195
...(ii)
On adding (i) and (ii) , we get
49
x
−
49
y
=
392
⇒
x
−
y
=
8
....(iii)
On subtracting (ii) from (i) , we get
x
+
y
=
2
....(iv)
On adding (iii) and (iv) , we get
2
x
=
10
⇒
x
=
5
By putting
x
=
5
in (iv), we get
5
+
y
=
2
⇒
y
=
−
3
Solve the following pair of equations
x
8
−
y
7
=
17
28
;
x
7
−
y
8
=
1
Report Question
0%
x
=
5
,
y
=
8
0%
x
=
19
,
y
=
8
0%
x
=
12
,
y
=
8
0%
x
=
14
,
y
=
8
Explanation
Given,
x
8
−
y
7
=
17
28
;
x
7
−
y
8
=
1
Rewriting the given equations, we get
7
x
−
8
y
=
34
...(i)
8
x
−
7
y
=
56
...(ii)
On multiplying (i) by 8 and (ii) by 7, we get
56
x
−
64
y
=
272
5
−
6
x
−
+
49
y
=
3
−
92
_
−
15
y
=
−
120
∴
y
=
8
On putting
y
=
8
in (i), we get
7
x
−
8
(
8
)
=
34
⇒
7
x
=
34
+
64
⇒
x
=
14
∴
x
=
14
,
y
=
8
Solve the following simultaneous equations:
2
x
3
+
y
4
=
12
;
4
x
3
−
9
y
4
=
2
Report Question
0%
x
=
12
,
y
=
5
0%
x
=
15
,
y
=
8
0%
x
=
13
,
y
=
4
0%
x
=
14
,
y
=
9
Explanation
Rewriting the given equations after taking LCM,
8
x
+
3
y
=
144
...
(
1
)
16
x
−
27
y
=
24
...
(
2
)
Multiplying
(
1
)
by
2
16
x
+
6
y
=
288
...
(
3
)
16
x
−
27
y
=
24
...
(
2
)
Subtracting
(
3
)
and
(
2
)
,
33
y
=
264
y
=
8
Substituting
y
=
8
in
(
1
)
, we get
8
x
+
24
=
144
8
x
=
120
x
=
15
x
=
15
,
y
=
8
Option
B
The ratio of the present ages of mother and son is
12
:
5
. The mother's age at the time of the birth of the son was
21
years. Find their present ages.
Report Question
0%
mother age
=
36
years, son age
=
15
years
0%
mother age
=
56
years, son age
=
5
years
0%
mother age
=
46
years, son age
=
25
years
0%
mother age
=
47
years, son age
=
26
years
Explanation
Let mother age be
M
and that of son age be
S
Therefore according to question,
M
=
S
+
21
...(1)
and
5
M
=
12
S
....(2)
Substitute equation (1) in equation (2), we get
5
(
S
+
21
)
=
12
S
⇒
5
S
+
105
=
12
S
⇒
7
S
=
105
⇒
S
=
15
Using equation (1), we get
M
=
15
+
21
=
36
Mother age is
36
years and Son age is
15
years.
A two-digit number is 3 more than six times the sum of its digits. If 18 is added to the number obtained by interchanged by interchanging the digits, we get the original number. Find the number.
Report Question
0%
25
0%
45
0%
75
0%
None of these
Explanation
Let the tens and the units digits in the number be
x
and
y
, respectively.
So, the number may be written as
10
x
+
y
.
According to the given condition.
10
x
+
y
=
6
(
x
+
y
)
+
3
⇒
4
x
−
5
y
=
3
.....(i)
If we interchange the digits of Original number then we get new number. i.e
10
y
+
x
According to the given condition
10
y
+
x
+
18
=
10
x
+
y
⇒
9
x
−
9
y
=
18
⇒
x
−
y
=
2
.....(ii)
Now multiplying equation (ii) by
4
. we get,
4
x
−
4
y
=
8
....(iii)
On subtracting (iii) from (i). we get,
4
x
−
5
y
−
(
4
x
−
4
y
)
=
3
−
8
∴
y
=
5
On substituting
y
=
5
in (ii). we get,
x
−
5
=
2
⇒
x
=
7
∴
number is
10
x
+
y
=
10
(
7
)
+
5
=
75
From the following figure, we can say:
2
x
3
+
3
y
2
=
8
1
3
;
3
x
2
+
2
y
3
=
13
1
3
Report Question
0%
x
=
1
,
y
=
4
0%
x
=
8
,
y
=
3
0%
x
=
6
,
y
=
5
0%
None of these
Explanation
2
x
3
+
3
y
2
=
8
1
3
⇒
4
x
+
9
y
6
=
25
3
⇒
4
x
+
9
y
=
50
.......(i)
3
x
2
+
2
y
3
=
13
1
3
⇒
9
x
+
4
y
6
=
40
3
⇒
9
x
+
4
y
=
80
......(ii)
Adding (i) and (ii). we get,
13
x
+
13
y
=
130
∴
x
+
y
=
10
......(iii)
On subtracting (i) from (ii). we get,
5
x
−
5
y
=
30
∴
x
−
y
=
6
......(iv)
Again adding (iii) and (iv). we get,
2
x
=
16
⇒
x
=
8
On substituting
x
=
8
in (iv). we get,
8
−
y
=
6
∴
y
=
2
∴
x
=
8
,
y
=
2
Point
A
and
B
are
70
k
m
apart on a highway. A car starts from
A
and another car starts from
B
at the same time. If they travel in the same direction, they meet in
7
hours, but if they travel towards each other they meet in one hour. What are their speeds?
Report Question
0%
30
k
m
/
h
r
and
40
k
m
/
h
r
0%
36
k
m
/
h
r
and
40
k
m
/
h
r
0%
19
k
m
/
h
r
and
20
k
m
/
h
r
0%
40
k
m
/
h
r
and
50
k
m
/
h
r
Explanation
Let car speed from point
A
=
x
k
m
/
h
r
.
and car speed from point
B
=
y
k
m
/
h
r
.
Distance = speed
×
time
∴
Distance from
A
=
x
×
7
=
7
x
Distance from
B
=
y
×
7
=
7
y
If they travel in the same direction, they meet in
7
hours. Point
A
and
B
are
70
k
m
apart.
⇒
7
x
−
7
y
=
70
⇒
x
−
y
=
10
...
(
i
)
if they travel towards each other they meet in one hour. Point
A
and
B
are
70
k
m
apart.
x
+
y
=
70
...
(
i
i
)
Adding
(
i
)
and
(
i
i
)
. we get
2
x
=
80
∴
x
=
40
substituting
x
=
40
in
(
i
)
. we get
40
−
y
=
10
∴
y
=
30
∴
x
=
40
k
m
/
h
r
and
y
=
30
k
m
/
h
r
.
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Practice Class 12 Commerce Applied Mathematics Quiz Questions and Answers
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