EduSahara™ Assignment
Name : Proportions Application
Chapter : Proportion
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
If
a,b,c,d,e,f
are in continued proportion, then which of the following is true?
(i)
a
b
=
b
c
=
c
d
(ii)
a
b
b
c
=
b
c
c
d
=
c
d
d
e
(iii)
a
b
=
c
d
=
e
f
(iv)
ab
=
bc
=
cd
=
de
Question
2
2.
If
a
b
=
c
d
=
e
f
,
then
(
a
+
c
+
e
)
(
b
+
d
+
f
)
=
(i)
2
(
a
+
b
+
c
)
(ii)
a
b
(iii)
1
(iv)
(
a
+
b
+
c
)
(v)
a
c
e
Question
3
3.
If
a
b
=
c
d
,
then which of the following is true ?
(i)
4
a
+
3
b
4
a
−
3
b
=
4
c
+
3
d
4
c
−
3
d
(ii)
4
a
+
2
b
4
a
−
2
d
=
4
c
+
3
d
4
c
−
2
d
(iii)
4
a
−
2
b
4
a
−
2
d
=
4
c
−
3
d
4
c
−
2
d
(iv)
4
a
+
3
d
4
a
−
3
d
=
3
b
+
4
c
3
b
−
4
c
Question
4
4.
If
x
b
−
c
=
y
c
−
a
=
z
a
−
b
,
then
(i)
a
x
+
b
y
+
c
z
=
0
(ii)
a
x
+
b
y
−
c
z
=
0
(iii)
a
x
−
b
y
+
c
z
=
0
(iv)
a
x
+
b
y
+
c
z
=
1
(v)
a
x
−
b
y
−
c
z
=
0
Question
5
5.
If
x
+
y
a
x
+
b
y
=
y
+
z
a
y
+
b
z
=
z
+
x
a
z
+
b
x
,
then each of the ratios is equal to
(i)
a+b
x+y
(ii)
1
(iii)
x+y
a+b
(iv)
(a+b)
2
(v)
2
(a+b)
Question
6
6.
If
a
b
+
c
=
b
c
+
a
=
c
a
+
b
where
a
+
b
+
c
≠
0,
then each of the ratios is equal to
(i)
2
(ii)
1
2
(iii)
-1
(iv)
(
-1
2
)
(v)
a + b + c
Question
7
7.
If
a
b
+
c
=
b
c
+
a
=
c
a
+
b
where
a
+
b
+
c
=
0,
then each of the ratios is equal to
(i)
2
(ii)
-1
(iii)
1
2
(iv)
(
-1
2
)
(v)
a + b + c
Question
8
8.
If
'b'
is the mean proportional between
'a'
and
'c'
,
then the mean proportional between
(
a
2
+
b
2
)
and
(
b
2
+
c
2
) is
(i)
a (b + c)
(ii)
b (a + c)
(iii)
ab + bc + ca
(iv)
c (a + b)
Question
9
9.
If
'a'
≠
'b'
and
'a'
:
'b'
is the duplicate ratio of (
'a'
+
'c'
) : (
'b'
+
'c'
),
then the mean proportional between
'a'
and
'b'
is
(i)
c
2
(ii)
c
2
(iii)
2c
(iv)
c
Question
10
10.
What
least number must be added to
19
,
7
,
11
,
3
so that the resulting numbers
are in proportion ?
(i)
5
(ii)
6
(iii)
4
(iv)
3
(v)
7
Question
11
11.
What
must be subtracted from
19
,
29
,
16
,
24
so that the resulting numbers
are in proportion ?
(i)
4
(ii)
6
(iii)
2
(iv)
3
(v)
5
Question
12
12.
If
'b'
is the mean proportion between
'a'
and
'c'
,
then
a
2
-
b
2
+
c
2
a
-2
-
b
-2
+
c
-2
=
(i)
b
2
(ii)
b
4
(iii)
b
-2
(iv)
a
2
(v)
c
2
Question
13
13.
If
(
a
3
+
12
a
)
(
6
a
2
+
8
)
=
1072
386
, find
a
(i)
17
(ii)
18
(iii)
15
(iv)
16
(v)
14
Question
14
14.
If
(
a
3
+
75
a
b
2
)
(
15
a
2
b
+
125
b
3
)
=
407
279
, find
a : b
(i)
55
:
5
(ii)
54
:
3
(iii)
55
:
3
(iv)
55
:
1
(v)
56
:
3
Question
15
15.
If
(
x
+
19
)
,
(
x
+
4
)
,
(
x
+
16
)
and
(
x
+
2
)
are in proportion,
find
x
(i)
(
26
,
25
)
(ii)
(
27
,
27
)
(iii)
(
28
,
28
)
(iv)
(
29
,
26
)
(v)
(
26
,
26
)
Question
16
16.
If
(
6
x
2
−
5
x
y
+
y
2
)
=
0
, find
x : y
(i)
1 : 3
or
0 : 2
(ii)
1 : 3
or
1 : 4
(iii)
0 : 3
or
1 : 2
(iv)
2 : 3
or
1 : 2
(v)
1 : 3
or
1 : 2
Question
17
17.
If
(
5
x
+
1
)
is the geometric mean of
(
2
x
+
2
)
and
(
10
x
+
2
)
,
find
x
(i)
(
1
5
,
3
)
(ii)
(
(
-1
7
)
,
4
)
(iii)
(
(
-1
5
)
,
2
)
(iv)
(
5
,
9
5
)
(v)
(
(
-1
5
)
,
3
)
Question
18
18.
If
10
,
x
,
160
are in continued proportion, find
x
(i)
39
(ii)
37
(iii)
40
(iv)
42
(v)
41
Question
19
19.
Find the mean proportional between
4.5
and
112.5
(i)
23.5
(ii)
20.5
(iii)
24.5
(iv)
21.5
(v)
22.5
Question
20
20.
Find the mean proportional between
√
9
and
15
(i)
3
√
2
(ii)
15
(iii)
3
4
√
5
(iv)
3
√
5
(v)
3
√
7
Question
21
21.
Solve
√
(
x
−
1
)
+
√
(
x
+
1
)
√
(
x
−
1
)
−
√
(
x
+
1
)
=
7
3
(i)
(
-29
21
)
(ii)
(
-31
21
)
(iii)
(
-9
7
)
(iv)
(
-31
23
)
(v)
(
-27
19
)
Question
22
22.
Find two numbers whose mean proportional is
14
and third proportional is
2401
4
(i)
6
and
49
(ii)
4
and
49
(iii)
5
and
49
(iv)
4
and
47
(v)
4
and
48
Assignment Key
1) (i)
2) (ii)
3) (i)
4) (i)
5) (v)
6) (ii)
7) (ii)
8) (ii)
9) (iv)
10) (i)
11) (i)
12) (ii)
13) (iv)
14) (iii)
15) (v)
16) (v)
17) (v)
18) (iii)
19) (v)
20) (iv)
21) (i)
22) (ii)
