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)
ab
=
bc
=
cd
=
de
(ii)
a
b
=
b
c
=
c
d
(iii)
a
b
b
c
=
b
c
c
d
=
c
d
d
e
(iv)
a
b
=
c
d
=
e
f
Question
2
2.
If
a
b
=
c
d
=
e
f
,
then
(
a
+
c
+
e
)
(
b
+
d
+
f
)
=
(i)
(
a
+
b
+
c
)
(ii)
2
(
a
+
b
+
c
)
(iii)
a
b
(iv)
a
c
e
(v)
1
Question
3
3.
If
a
b
=
c
d
,
then which of the following is true ?
(i)
5
a
+
4
b
5
a
−
4
d
=
5
c
+
3
d
5
c
−
4
d
(ii)
5
a
+
3
b
5
a
−
3
b
=
5
c
+
3
d
5
c
−
3
d
(iii)
5
a
+
3
d
5
a
−
3
d
=
3
b
+
5
c
3
b
−
5
c
(iv)
5
a
−
4
b
5
a
−
4
d
=
5
c
−
3
d
5
c
−
4
d
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
=
1
(iv)
a
x
+
b
y
+
c
z
=
0
(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)
2
(ii)
2
(a+b)
(iii)
1
(iv)
a+b
x+y
(v)
x+y
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)
1
2
(ii)
-1
(iii)
2
(iv)
a + b + c
(v)
(
-1
2
)
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)
1
2
(ii)
2
(iii)
a + b + c
(iv)
(
-1
2
)
(v)
-1
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)
c (a + b)
(iii)
ab + bc + ca
(iv)
b (a + c)
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
6
,
24
,
0
,
9
so that the resulting numbers
are in proportion ?
(i)
3
(ii)
9
(iii)
6
(iv)
5
(v)
7
Question
11
11.
What
must be subtracted from
30
,
21
,
54
,
36
so that the resulting numbers
are in proportion ?
(i)
7
(ii)
5
(iii)
6
(iv)
9
(v)
4
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
4
(ii)
b
2
(iii)
a
2
(iv)
c
2
(v)
b
-2
Question
13
13.
If
(
a
3
+
3
a
)
(
3
a
2
+
1
)
=
341
91
, find
a
(i)
12
(ii)
10
(iii)
13
(iv)
8
(v)
11
Question
14
14.
If
(
a
3
+
27
a
b
2
)
(
9
a
2
b
+
27
b
3
)
=
520
504
, find
a : b
(i)
4
:
1
(ii)
6
:
1
(iii)
5
:
4
(iv)
5
:
1
(v)
5
:
-1
Question
15
15.
If
(
4
x
+
10
)
,
(
3
x
+
3
)
,
(
5
x
+
5
)
and
(
3
x
+
7
)
are in proportion,
find
x
(i)
(
-1
,
11
)
(ii)
(
(
-5
3
)
,
11
)
(iii)
(
(
-5
3
)
,
10
)
(iv)
(
(
-7
5
)
,
12
)
(v)
(
13
,
1
3
)
Question
16
16.
If
(
16
x
2
−
40
x
y
+
25
y
2
)
=
0
, find
x : y
(i)
6 : 4
or
5 : 4
(ii)
4 : 4
or
5 : 4
(iii)
5 : 4
or
4 : 4
(iv)
5 : 4
or
5 : 4
(v)
5 : 4
or
5 : 7
Question
17
17.
If
(
3
x
+
3
)
is the geometric mean of
(
x
+
4
)
and
(
7
x
+
1
)
,
find
x
(i)
(
7
,
7
2
)
(ii)
(
1
2
,
5
)
(iii)
(
1
2
,
4
)
(iv)
(
3
2
,
5
)
(v)
(
1
4
,
6
)
Question
18
18.
If
7
,
x
,
28
are in continued proportion, find
x
(i)
12
(ii)
16
(iii)
13
(iv)
14
(v)
15
Question
19
19.
Find the mean proportional between
2.7
and
97.2
(i)
16.2
(ii)
15.2
(iii)
14.2
(iv)
18.2
(v)
17.2
Question
20
20.
Find the mean proportional between
√
5
and
√
45
(i)
15
(ii)
4
√
15
(iii)
√
18
(iv)
√
15
(v)
√
12
Question
21
21.
Solve
√
(
x
+
2
)
+
√
(
x
+
3
)
√
(
x
+
2
)
−
√
(
x
+
3
)
=
4
2
(i)
(
-25
8
)
(ii)
(
-19
6
)
(iii)
(
-27
8
)
(iv)
(
-31
10
)
(v)
(
-23
8
)
Question
22
22.
Find two numbers whose mean proportional is
12
and third proportional is
768
(i)
3
and
47
(ii)
5
and
48
(iii)
4
and
48
(iv)
3
and
48
(v)
3
and
46
Assignment Key
1) (ii)
2) (iii)
3) (ii)
4) (iv)
5) (ii)
6) (i)
7) (v)
8) (iv)
9) (iv)
10) (iii)
11) (iii)
12) (i)
13) (v)
14) (iv)
15) (ii)
16) (iv)
17) (ii)
18) (iv)
19) (i)
20) (iv)
21) (i)
22) (iv)
