Class 7 Exam > Class 7 Notes > Mathematics (Maths) Class 7 > RS Aggarwal Solutions: Ratio and Proportion
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Page 1
Q u e s t i o n : 1
Express each of the following ratios in simplest form:
i
24 : 40
ii
13.5 : 15
iii
6
2
3
: 7
1
2
iv
1
6
:
1
9
v
4: 5:
9
2
vi
2.5 : 6.5 : 8
S o l u t i o n :
i
HCF of 24 and 40 is 8.
? 24 : 40 =
24
40
=
24 ÷ 8
40 ÷ 8
=
3
5
= 3 : 5
Hence, 24 : 40 in its simplest form is 3 : 5.
ii
HCF of 13.5 and 15 is 1.5.
13.5
15
=
135
150
The HCF of 135 and 150 is 15. =
135 ÷ 15
150 ÷ 15
=
9
10
Hence, 13.5 : 15 in its simplest form is 9 : 10.
iii
20
3
:
15
2
= 40 : 45
The HCF of 40 and 45 is 5.
? 40 : 45 =
40
45
=
40 ÷ 5
45 ÷ 5
=
8
9
= 8 : 9
Hence, 6
2
3
: 7
1
2
in its simplest form is 8 : 9
(iv) 9 : 6
The HCF of 9 and 6 is 3.
? 9 : 6 =
9
6
=
9 ÷ 3
6 ÷ 3
= 3 : 2
Hence,
1
6
:
1
9
in its simplest form is 3 : 2.
(v) LCM of the denominators is 2.
? 4 : 5 :
9
2
= 8 : 10 : 9
The HCF of these 3 numbers is 1.
? 8 : 10 : 9 is the simplest form.
vi
2.5 : 6.5 : 8 = 25 : 65 : 80
The HCF of 25, 65 and 80 is 5.
? 25 : 65 : 80 =
25
65
80
=
25 ÷ 5
65 ÷ 5
80 ÷ 5
=
5
13
16
= 5 : 13 : 16
Q u e s t i o n : 2
Express each of the following ratios in simplest form:
i
75 paise : 3 rupees
ii
Page 2
Q u e s t i o n : 1
Express each of the following ratios in simplest form:
i
24 : 40
ii
13.5 : 15
iii
6
2
3
: 7
1
2
iv
1
6
:
1
9
v
4: 5:
9
2
vi
2.5 : 6.5 : 8
S o l u t i o n :
i
HCF of 24 and 40 is 8.
? 24 : 40 =
24
40
=
24 ÷ 8
40 ÷ 8
=
3
5
= 3 : 5
Hence, 24 : 40 in its simplest form is 3 : 5.
ii
HCF of 13.5 and 15 is 1.5.
13.5
15
=
135
150
The HCF of 135 and 150 is 15. =
135 ÷ 15
150 ÷ 15
=
9
10
Hence, 13.5 : 15 in its simplest form is 9 : 10.
iii
20
3
:
15
2
= 40 : 45
The HCF of 40 and 45 is 5.
? 40 : 45 =
40
45
=
40 ÷ 5
45 ÷ 5
=
8
9
= 8 : 9
Hence, 6
2
3
: 7
1
2
in its simplest form is 8 : 9
(iv) 9 : 6
The HCF of 9 and 6 is 3.
? 9 : 6 =
9
6
=
9 ÷ 3
6 ÷ 3
= 3 : 2
Hence,
1
6
:
1
9
in its simplest form is 3 : 2.
(v) LCM of the denominators is 2.
? 4 : 5 :
9
2
= 8 : 10 : 9
The HCF of these 3 numbers is 1.
? 8 : 10 : 9 is the simplest form.
vi
2.5 : 6.5 : 8 = 25 : 65 : 80
The HCF of 25, 65 and 80 is 5.
? 25 : 65 : 80 =
25
65
80
=
25 ÷ 5
65 ÷ 5
80 ÷ 5
=
5
13
16
= 5 : 13 : 16
Q u e s t i o n : 2
Express each of the following ratios in simplest form:
i
75 paise : 3 rupees
ii
1 m 5 cm : 63 cm
iii
1 hour 5 minutes : 45 minutes
iv
8 months : 1 year
v
2kg250g
: 3kg
vi
1 km : 750 m
S o l u t i o n :
i
Converting both the quantities into the same unit, we have:
75 paise : (3 ×
100) paise = 75 : 300
=
75
300
=
75 ÷ 75
300 ÷ 75
=
1
4
? HCFof75and300 = 75
= 1 paise : 4 paise
ii
Converting both the quantities into the same unit, we have:
105 cm : 63 cm =
105
63
=
105÷21
63÷21
=
5
3
? HCFof105and63 = 21
= 5 cm : 3 cm
iii
Converting both the quantities into the same unit
65 min : 45 min =
65
45
=
65÷5
45÷5
=
13
9
? HCFof65and45 = 5
= 13 min : 9 min
iv
Converting both the quantities into the same unit, we get:
8 months : 12 months =
8
12
=
8÷4
12÷4
=
2
3
? HCFof8and12 = 4
= 2 months : 3 months
v
Converting both the quantities into the same unit, we get:
2250g : 3000 g =
2250
3000
=
2250÷750
3000÷750
=
3
4
? HCFof2250and3000 = 750
= 3 g : 4 g
vi
Converting both the quantities into the same unit, we get:
1000 m : 750 m =
1000
750
=
1000÷250
750÷250
=
4
3
? HCFof1000and750 = 250
= 4 m : 3 m
Q u e s t i o n : 3
If A : B = 7 : 5 and B : C = 9 : 14, find A : C.
S o l u t i o n :
A
B
=
7
5
and
B
C
=
9
14
Therefore, we have:
A
B
×
B
C
=
7
5
×
9
14
A
C
=
9
10
? A : C = 9 : 10
Q u e s t i o n : 4
If A : B = 5 : 8 and B : C = 16 : 25, find A : C.
S o l u t i o n :
A
B
=
5
8
and
B
C
=
16
25
Now, we have:
A
B
×
B
C
=
5
8
×
16
25
?
A
C
=
2
5
? A : C = 2 : 5
Q u e s t i o n : 5
If A : B = 3 : 5 and B : C = 10 : 13, find A : B : C.
S o l u t i o n :
A : B = 3 : 5
Page 3
Q u e s t i o n : 1
Express each of the following ratios in simplest form:
i
24 : 40
ii
13.5 : 15
iii
6
2
3
: 7
1
2
iv
1
6
:
1
9
v
4: 5:
9
2
vi
2.5 : 6.5 : 8
S o l u t i o n :
i
HCF of 24 and 40 is 8.
? 24 : 40 =
24
40
=
24 ÷ 8
40 ÷ 8
=
3
5
= 3 : 5
Hence, 24 : 40 in its simplest form is 3 : 5.
ii
HCF of 13.5 and 15 is 1.5.
13.5
15
=
135
150
The HCF of 135 and 150 is 15. =
135 ÷ 15
150 ÷ 15
=
9
10
Hence, 13.5 : 15 in its simplest form is 9 : 10.
iii
20
3
:
15
2
= 40 : 45
The HCF of 40 and 45 is 5.
? 40 : 45 =
40
45
=
40 ÷ 5
45 ÷ 5
=
8
9
= 8 : 9
Hence, 6
2
3
: 7
1
2
in its simplest form is 8 : 9
(iv) 9 : 6
The HCF of 9 and 6 is 3.
? 9 : 6 =
9
6
=
9 ÷ 3
6 ÷ 3
= 3 : 2
Hence,
1
6
:
1
9
in its simplest form is 3 : 2.
(v) LCM of the denominators is 2.
? 4 : 5 :
9
2
= 8 : 10 : 9
The HCF of these 3 numbers is 1.
? 8 : 10 : 9 is the simplest form.
vi
2.5 : 6.5 : 8 = 25 : 65 : 80
The HCF of 25, 65 and 80 is 5.
? 25 : 65 : 80 =
25
65
80
=
25 ÷ 5
65 ÷ 5
80 ÷ 5
=
5
13
16
= 5 : 13 : 16
Q u e s t i o n : 2
Express each of the following ratios in simplest form:
i
75 paise : 3 rupees
ii
1 m 5 cm : 63 cm
iii
1 hour 5 minutes : 45 minutes
iv
8 months : 1 year
v
2kg250g
: 3kg
vi
1 km : 750 m
S o l u t i o n :
i
Converting both the quantities into the same unit, we have:
75 paise : (3 ×
100) paise = 75 : 300
=
75
300
=
75 ÷ 75
300 ÷ 75
=
1
4
? HCFof75and300 = 75
= 1 paise : 4 paise
ii
Converting both the quantities into the same unit, we have:
105 cm : 63 cm =
105
63
=
105÷21
63÷21
=
5
3
? HCFof105and63 = 21
= 5 cm : 3 cm
iii
Converting both the quantities into the same unit
65 min : 45 min =
65
45
=
65÷5
45÷5
=
13
9
? HCFof65and45 = 5
= 13 min : 9 min
iv
Converting both the quantities into the same unit, we get:
8 months : 12 months =
8
12
=
8÷4
12÷4
=
2
3
? HCFof8and12 = 4
= 2 months : 3 months
v
Converting both the quantities into the same unit, we get:
2250g : 3000 g =
2250
3000
=
2250÷750
3000÷750
=
3
4
? HCFof2250and3000 = 750
= 3 g : 4 g
vi
Converting both the quantities into the same unit, we get:
1000 m : 750 m =
1000
750
=
1000÷250
750÷250
=
4
3
? HCFof1000and750 = 250
= 4 m : 3 m
Q u e s t i o n : 3
If A : B = 7 : 5 and B : C = 9 : 14, find A : C.
S o l u t i o n :
A
B
=
7
5
and
B
C
=
9
14
Therefore, we have:
A
B
×
B
C
=
7
5
×
9
14
A
C
=
9
10
? A : C = 9 : 10
Q u e s t i o n : 4
If A : B = 5 : 8 and B : C = 16 : 25, find A : C.
S o l u t i o n :
A
B
=
5
8
and
B
C
=
16
25
Now, we have:
A
B
×
B
C
=
5
8
×
16
25
?
A
C
=
2
5
? A : C = 2 : 5
Q u e s t i o n : 5
If A : B = 3 : 5 and B : C = 10 : 13, find A : B : C.
S o l u t i o n :
A : B = 3 : 5
B : C = 10 : 13 =
10÷2
13÷2
= 5 :
13
2
Now, A : B : C = 3 : 5 :
13
2
? A : B : C = 6 : 10 : 13
Q u e s t i o n : 6
If A : B = 5 : 6 and B : C = 4 : 7, find A : B : C.
S o l u t i o n :
We have the following:
A : B = 5 : 6
B : C = 4 : 7 =
4
7
=
4×
6
4
7×
6
4
= 6 :
21
2
? A : B : C = 5 : 6 :
21
2
= 10 : 12 : 21
Q u e s t i o n : 7
Divide Rs 360 between Kunal and Mohit in the ratio 7 : 8.
S o l u t i o n :
Sum of the ratio terms = 7 + 8 = 15
Now, we have the following:
Kunal's share = Rs 360 ×
7
15
= 24 ×7
= Rs 168
Mohit's share = Rs 360 ×
8
15
= 24 ×8
= Rs 192
Q u e s t i o n : 8
Divide Rs 880 between Rajan and Kamal in the ratio
1
5
:
1
6
.
S o l u t i o n :
Sum of the ratio terms =
1
5
+
1
6
=
11
30
Now, we have the following:
Rajan's share = Rs 880 ×
1
5
11
30
= Rs 880 ×
6
11
= Rs 80 ×6
= Rs 480
Kamal's share = Rs 880 ×
1
6
11
30
= Rs 880 ×
5
11
= Rs 80 ×5
= Rs 400
Q u e s t i o n : 9
Divide Rs 5600 between A, B and C in the ratio 1 : 3 : 4.
S o l u t i o n :
Sum of the ratio terms is 1 +3 +4
= 8
We have the following:
A's share = Rs 5600 ×
1
8
= Rs
5600
8
= Rs 700
B's share = Rs 5600 ×
3
8
= Rs 700 × 3
= Rs 2100
C's share = Rs 5600 ×
4
8
= Rs 700 ×4
= Rs 2800
Q u e s t i o n : 1 0
What number must be added to each term to the ratio 9 : 16 to make the ratio 2 : 3?
S o l u t i o n :
Let x be the required number.
Then, (9 + x) : (16 + x) = 2 : 3
?
9+x
16+x
=
2
3
? 27 + 3x = 32 + 2x ? x = 5
Hence, 5 must be added to each term of the ratio 9 : 16 to make it 2 : 3.
Q u e s t i o n : 1 1
Page 4
Q u e s t i o n : 1
Express each of the following ratios in simplest form:
i
24 : 40
ii
13.5 : 15
iii
6
2
3
: 7
1
2
iv
1
6
:
1
9
v
4: 5:
9
2
vi
2.5 : 6.5 : 8
S o l u t i o n :
i
HCF of 24 and 40 is 8.
? 24 : 40 =
24
40
=
24 ÷ 8
40 ÷ 8
=
3
5
= 3 : 5
Hence, 24 : 40 in its simplest form is 3 : 5.
ii
HCF of 13.5 and 15 is 1.5.
13.5
15
=
135
150
The HCF of 135 and 150 is 15. =
135 ÷ 15
150 ÷ 15
=
9
10
Hence, 13.5 : 15 in its simplest form is 9 : 10.
iii
20
3
:
15
2
= 40 : 45
The HCF of 40 and 45 is 5.
? 40 : 45 =
40
45
=
40 ÷ 5
45 ÷ 5
=
8
9
= 8 : 9
Hence, 6
2
3
: 7
1
2
in its simplest form is 8 : 9
(iv) 9 : 6
The HCF of 9 and 6 is 3.
? 9 : 6 =
9
6
=
9 ÷ 3
6 ÷ 3
= 3 : 2
Hence,
1
6
:
1
9
in its simplest form is 3 : 2.
(v) LCM of the denominators is 2.
? 4 : 5 :
9
2
= 8 : 10 : 9
The HCF of these 3 numbers is 1.
? 8 : 10 : 9 is the simplest form.
vi
2.5 : 6.5 : 8 = 25 : 65 : 80
The HCF of 25, 65 and 80 is 5.
? 25 : 65 : 80 =
25
65
80
=
25 ÷ 5
65 ÷ 5
80 ÷ 5
=
5
13
16
= 5 : 13 : 16
Q u e s t i o n : 2
Express each of the following ratios in simplest form:
i
75 paise : 3 rupees
ii
1 m 5 cm : 63 cm
iii
1 hour 5 minutes : 45 minutes
iv
8 months : 1 year
v
2kg250g
: 3kg
vi
1 km : 750 m
S o l u t i o n :
i
Converting both the quantities into the same unit, we have:
75 paise : (3 ×
100) paise = 75 : 300
=
75
300
=
75 ÷ 75
300 ÷ 75
=
1
4
? HCFof75and300 = 75
= 1 paise : 4 paise
ii
Converting both the quantities into the same unit, we have:
105 cm : 63 cm =
105
63
=
105÷21
63÷21
=
5
3
? HCFof105and63 = 21
= 5 cm : 3 cm
iii
Converting both the quantities into the same unit
65 min : 45 min =
65
45
=
65÷5
45÷5
=
13
9
? HCFof65and45 = 5
= 13 min : 9 min
iv
Converting both the quantities into the same unit, we get:
8 months : 12 months =
8
12
=
8÷4
12÷4
=
2
3
? HCFof8and12 = 4
= 2 months : 3 months
v
Converting both the quantities into the same unit, we get:
2250g : 3000 g =
2250
3000
=
2250÷750
3000÷750
=
3
4
? HCFof2250and3000 = 750
= 3 g : 4 g
vi
Converting both the quantities into the same unit, we get:
1000 m : 750 m =
1000
750
=
1000÷250
750÷250
=
4
3
? HCFof1000and750 = 250
= 4 m : 3 m
Q u e s t i o n : 3
If A : B = 7 : 5 and B : C = 9 : 14, find A : C.
S o l u t i o n :
A
B
=
7
5
and
B
C
=
9
14
Therefore, we have:
A
B
×
B
C
=
7
5
×
9
14
A
C
=
9
10
? A : C = 9 : 10
Q u e s t i o n : 4
If A : B = 5 : 8 and B : C = 16 : 25, find A : C.
S o l u t i o n :
A
B
=
5
8
and
B
C
=
16
25
Now, we have:
A
B
×
B
C
=
5
8
×
16
25
?
A
C
=
2
5
? A : C = 2 : 5
Q u e s t i o n : 5
If A : B = 3 : 5 and B : C = 10 : 13, find A : B : C.
S o l u t i o n :
A : B = 3 : 5
B : C = 10 : 13 =
10÷2
13÷2
= 5 :
13
2
Now, A : B : C = 3 : 5 :
13
2
? A : B : C = 6 : 10 : 13
Q u e s t i o n : 6
If A : B = 5 : 6 and B : C = 4 : 7, find A : B : C.
S o l u t i o n :
We have the following:
A : B = 5 : 6
B : C = 4 : 7 =
4
7
=
4×
6
4
7×
6
4
= 6 :
21
2
? A : B : C = 5 : 6 :
21
2
= 10 : 12 : 21
Q u e s t i o n : 7
Divide Rs 360 between Kunal and Mohit in the ratio 7 : 8.
S o l u t i o n :
Sum of the ratio terms = 7 + 8 = 15
Now, we have the following:
Kunal's share = Rs 360 ×
7
15
= 24 ×7
= Rs 168
Mohit's share = Rs 360 ×
8
15
= 24 ×8
= Rs 192
Q u e s t i o n : 8
Divide Rs 880 between Rajan and Kamal in the ratio
1
5
:
1
6
.
S o l u t i o n :
Sum of the ratio terms =
1
5
+
1
6
=
11
30
Now, we have the following:
Rajan's share = Rs 880 ×
1
5
11
30
= Rs 880 ×
6
11
= Rs 80 ×6
= Rs 480
Kamal's share = Rs 880 ×
1
6
11
30
= Rs 880 ×
5
11
= Rs 80 ×5
= Rs 400
Q u e s t i o n : 9
Divide Rs 5600 between A, B and C in the ratio 1 : 3 : 4.
S o l u t i o n :
Sum of the ratio terms is 1 +3 +4
= 8
We have the following:
A's share = Rs 5600 ×
1
8
= Rs
5600
8
= Rs 700
B's share = Rs 5600 ×
3
8
= Rs 700 × 3
= Rs 2100
C's share = Rs 5600 ×
4
8
= Rs 700 ×4
= Rs 2800
Q u e s t i o n : 1 0
What number must be added to each term to the ratio 9 : 16 to make the ratio 2 : 3?
S o l u t i o n :
Let x be the required number.
Then, (9 + x) : (16 + x) = 2 : 3
?
9+x
16+x
=
2
3
? 27 + 3x = 32 + 2x ? x = 5
Hence, 5 must be added to each term of the ratio 9 : 16 to make it 2 : 3.
Q u e s t i o n : 1 1
What number must be subtracted from each term of ratio 17 : 33 so that the ratio becomes 7 : 15?
S o l u t i o n :
Suppose that x is the number that must be subtracted.
Then, (17 - x) : (33 - x) = 7 : 15
?
17 - x
33 - x
=
7
15
? 255 - 15x = 231 - 7x ? 8x = 255 - 231 = 24 ? x = 3
Hence, 3 must be subtracted from each term of ratio 17 : 33 so that it becomes 7 : 15.
Q u e s t i o n : 1 2
Two numbers are in the ratio 7 : 11. If added to each of the numbers, the ratio becomes 2 : 3. Find the numbers.
S o l u t i o n :
Suppose that the numbers are 7x and 11x.
Then, (7x + 7) : (11x + 7) = 2 : 3
?
7x + 7
11x + 7
=
2
3
? 21x + 21 = 22x + 14
? x = 7
Hence, the numbers are (7 ×
7 =) 49 and (11 ×
7 =) 77.
Q u e s t i o n : 1 3
Two numbers are in the ratio 5 : 9. On subtracting 3 from each, the ratio becomes 1 : 2. Find the numbers.
S o l u t i o n :
Suppose that the numbers are 5x and 9x.
Then, (5x - 3) : (9x - 3) = 1 : 2
?
5x - 3
9x -3
=
1
2
? 10x - 6 = 9x - 3
? x = 3
Hence, the numbers are (5 ×
3 =) 15 and (9 ×
3 =) 27.
Q u e s t i o n : 1 4
Two numbers are in the ratio 3 : 4. If their LCM is 180, find the numbers.
S o l u t i o n :
Let the numbers be 3x and 4x.
Their LCM is 12x.
Then, 12x = 180
? x = 15
? The numbers are (3 ×
15 =) 45 and (4 ×
15 =) 60.
Q u e s t i o n : 1 5
The ages of A and B are in the ratio 8 : 3. Six years hence, their ages will be in the ratio 9 : 4. Find their present ages.
S o l u t i o n :
Suppose that the present ages of A and B are 8x yrs and 3x yrs.
Then, (8x + 6) : (3x + 6) = 9 : 4
?
8x+6
3x+6
=
9
4
? 32x + 24 = 27x + 54
? 5x = 30
? x = 6
Now, present age of A = 8 ×
6 yrs = 48 yrs
Present age of B = 3 ×
6 yrs = 18 yrs
Q u e s t i o n : 1 6
The ratio of copper and zinc in an alloy is 9 : 5. If the weight of copper in the alloy is 48.6 grams, find the weight of zinc in the alloy.
S o l u t i o n :
Suppose that the weight of zinc is x g.
Then, 48.6 : x = 9 : 5
? x =
48.6×5
9
=
243
9
= 27
Hence, the weight of zinc in the alloy is 27 g.
Q u e s t i o n : 1 7
The ratio of boys and girls in a school is 8 : 3. If the total number of girls be 375, find the number of boys in the school.
Page 5
Q u e s t i o n : 1
Express each of the following ratios in simplest form:
i
24 : 40
ii
13.5 : 15
iii
6
2
3
: 7
1
2
iv
1
6
:
1
9
v
4: 5:
9
2
vi
2.5 : 6.5 : 8
S o l u t i o n :
i
HCF of 24 and 40 is 8.
? 24 : 40 =
24
40
=
24 ÷ 8
40 ÷ 8
=
3
5
= 3 : 5
Hence, 24 : 40 in its simplest form is 3 : 5.
ii
HCF of 13.5 and 15 is 1.5.
13.5
15
=
135
150
The HCF of 135 and 150 is 15. =
135 ÷ 15
150 ÷ 15
=
9
10
Hence, 13.5 : 15 in its simplest form is 9 : 10.
iii
20
3
:
15
2
= 40 : 45
The HCF of 40 and 45 is 5.
? 40 : 45 =
40
45
=
40 ÷ 5
45 ÷ 5
=
8
9
= 8 : 9
Hence, 6
2
3
: 7
1
2
in its simplest form is 8 : 9
(iv) 9 : 6
The HCF of 9 and 6 is 3.
? 9 : 6 =
9
6
=
9 ÷ 3
6 ÷ 3
= 3 : 2
Hence,
1
6
:
1
9
in its simplest form is 3 : 2.
(v) LCM of the denominators is 2.
? 4 : 5 :
9
2
= 8 : 10 : 9
The HCF of these 3 numbers is 1.
? 8 : 10 : 9 is the simplest form.
vi
2.5 : 6.5 : 8 = 25 : 65 : 80
The HCF of 25, 65 and 80 is 5.
? 25 : 65 : 80 =
25
65
80
=
25 ÷ 5
65 ÷ 5
80 ÷ 5
=
5
13
16
= 5 : 13 : 16
Q u e s t i o n : 2
Express each of the following ratios in simplest form:
i
75 paise : 3 rupees
ii
1 m 5 cm : 63 cm
iii
1 hour 5 minutes : 45 minutes
iv
8 months : 1 year
v
2kg250g
: 3kg
vi
1 km : 750 m
S o l u t i o n :
i
Converting both the quantities into the same unit, we have:
75 paise : (3 ×
100) paise = 75 : 300
=
75
300
=
75 ÷ 75
300 ÷ 75
=
1
4
? HCFof75and300 = 75
= 1 paise : 4 paise
ii
Converting both the quantities into the same unit, we have:
105 cm : 63 cm =
105
63
=
105÷21
63÷21
=
5
3
? HCFof105and63 = 21
= 5 cm : 3 cm
iii
Converting both the quantities into the same unit
65 min : 45 min =
65
45
=
65÷5
45÷5
=
13
9
? HCFof65and45 = 5
= 13 min : 9 min
iv
Converting both the quantities into the same unit, we get:
8 months : 12 months =
8
12
=
8÷4
12÷4
=
2
3
? HCFof8and12 = 4
= 2 months : 3 months
v
Converting both the quantities into the same unit, we get:
2250g : 3000 g =
2250
3000
=
2250÷750
3000÷750
=
3
4
? HCFof2250and3000 = 750
= 3 g : 4 g
vi
Converting both the quantities into the same unit, we get:
1000 m : 750 m =
1000
750
=
1000÷250
750÷250
=
4
3
? HCFof1000and750 = 250
= 4 m : 3 m
Q u e s t i o n : 3
If A : B = 7 : 5 and B : C = 9 : 14, find A : C.
S o l u t i o n :
A
B
=
7
5
and
B
C
=
9
14
Therefore, we have:
A
B
×
B
C
=
7
5
×
9
14
A
C
=
9
10
? A : C = 9 : 10
Q u e s t i o n : 4
If A : B = 5 : 8 and B : C = 16 : 25, find A : C.
S o l u t i o n :
A
B
=
5
8
and
B
C
=
16
25
Now, we have:
A
B
×
B
C
=
5
8
×
16
25
?
A
C
=
2
5
? A : C = 2 : 5
Q u e s t i o n : 5
If A : B = 3 : 5 and B : C = 10 : 13, find A : B : C.
S o l u t i o n :
A : B = 3 : 5
B : C = 10 : 13 =
10÷2
13÷2
= 5 :
13
2
Now, A : B : C = 3 : 5 :
13
2
? A : B : C = 6 : 10 : 13
Q u e s t i o n : 6
If A : B = 5 : 6 and B : C = 4 : 7, find A : B : C.
S o l u t i o n :
We have the following:
A : B = 5 : 6
B : C = 4 : 7 =
4
7
=
4×
6
4
7×
6
4
= 6 :
21
2
? A : B : C = 5 : 6 :
21
2
= 10 : 12 : 21
Q u e s t i o n : 7
Divide Rs 360 between Kunal and Mohit in the ratio 7 : 8.
S o l u t i o n :
Sum of the ratio terms = 7 + 8 = 15
Now, we have the following:
Kunal's share = Rs 360 ×
7
15
= 24 ×7
= Rs 168
Mohit's share = Rs 360 ×
8
15
= 24 ×8
= Rs 192
Q u e s t i o n : 8
Divide Rs 880 between Rajan and Kamal in the ratio
1
5
:
1
6
.
S o l u t i o n :
Sum of the ratio terms =
1
5
+
1
6
=
11
30
Now, we have the following:
Rajan's share = Rs 880 ×
1
5
11
30
= Rs 880 ×
6
11
= Rs 80 ×6
= Rs 480
Kamal's share = Rs 880 ×
1
6
11
30
= Rs 880 ×
5
11
= Rs 80 ×5
= Rs 400
Q u e s t i o n : 9
Divide Rs 5600 between A, B and C in the ratio 1 : 3 : 4.
S o l u t i o n :
Sum of the ratio terms is 1 +3 +4
= 8
We have the following:
A's share = Rs 5600 ×
1
8
= Rs
5600
8
= Rs 700
B's share = Rs 5600 ×
3
8
= Rs 700 × 3
= Rs 2100
C's share = Rs 5600 ×
4
8
= Rs 700 ×4
= Rs 2800
Q u e s t i o n : 1 0
What number must be added to each term to the ratio 9 : 16 to make the ratio 2 : 3?
S o l u t i o n :
Let x be the required number.
Then, (9 + x) : (16 + x) = 2 : 3
?
9+x
16+x
=
2
3
? 27 + 3x = 32 + 2x ? x = 5
Hence, 5 must be added to each term of the ratio 9 : 16 to make it 2 : 3.
Q u e s t i o n : 1 1
What number must be subtracted from each term of ratio 17 : 33 so that the ratio becomes 7 : 15?
S o l u t i o n :
Suppose that x is the number that must be subtracted.
Then, (17 - x) : (33 - x) = 7 : 15
?
17 - x
33 - x
=
7
15
? 255 - 15x = 231 - 7x ? 8x = 255 - 231 = 24 ? x = 3
Hence, 3 must be subtracted from each term of ratio 17 : 33 so that it becomes 7 : 15.
Q u e s t i o n : 1 2
Two numbers are in the ratio 7 : 11. If added to each of the numbers, the ratio becomes 2 : 3. Find the numbers.
S o l u t i o n :
Suppose that the numbers are 7x and 11x.
Then, (7x + 7) : (11x + 7) = 2 : 3
?
7x + 7
11x + 7
=
2
3
? 21x + 21 = 22x + 14
? x = 7
Hence, the numbers are (7 ×
7 =) 49 and (11 ×
7 =) 77.
Q u e s t i o n : 1 3
Two numbers are in the ratio 5 : 9. On subtracting 3 from each, the ratio becomes 1 : 2. Find the numbers.
S o l u t i o n :
Suppose that the numbers are 5x and 9x.
Then, (5x - 3) : (9x - 3) = 1 : 2
?
5x - 3
9x -3
=
1
2
? 10x - 6 = 9x - 3
? x = 3
Hence, the numbers are (5 ×
3 =) 15 and (9 ×
3 =) 27.
Q u e s t i o n : 1 4
Two numbers are in the ratio 3 : 4. If their LCM is 180, find the numbers.
S o l u t i o n :
Let the numbers be 3x and 4x.
Their LCM is 12x.
Then, 12x = 180
? x = 15
? The numbers are (3 ×
15 =) 45 and (4 ×
15 =) 60.
Q u e s t i o n : 1 5
The ages of A and B are in the ratio 8 : 3. Six years hence, their ages will be in the ratio 9 : 4. Find their present ages.
S o l u t i o n :
Suppose that the present ages of A and B are 8x yrs and 3x yrs.
Then, (8x + 6) : (3x + 6) = 9 : 4
?
8x+6
3x+6
=
9
4
? 32x + 24 = 27x + 54
? 5x = 30
? x = 6
Now, present age of A = 8 ×
6 yrs = 48 yrs
Present age of B = 3 ×
6 yrs = 18 yrs
Q u e s t i o n : 1 6
The ratio of copper and zinc in an alloy is 9 : 5. If the weight of copper in the alloy is 48.6 grams, find the weight of zinc in the alloy.
S o l u t i o n :
Suppose that the weight of zinc is x g.
Then, 48.6 : x = 9 : 5
? x =
48.6×5
9
=
243
9
= 27
Hence, the weight of zinc in the alloy is 27 g.
Q u e s t i o n : 1 7
The ratio of boys and girls in a school is 8 : 3. If the total number of girls be 375, find the number of boys in the school.
S o l u t i o n :
Suppose that the number of boys is x.
Then, x : 375 = 8 : 3
? x =
8×375
3
= 8 ×125
= 1000
Hence, the number of girls in the school is 1000.
Q u e s t i o n : 1 8
The ratio of monthly income to the savings of a family is 11 : 2. If the savings be Rs 2500, find the income and expenditure.
S o l u t i o n :
Suppose that the monthly income of the family is Rs x.
Then, x : 2500 = 11 : 2
? x =
11×2500
2
= 11 ×1250
? x = Rs 13750
Hence, the income is Rs 13,750.
? Expenditure = monthlyincome -savings
=Rs 13750 -2500
= Rs 11250
Q u e s t i o n : 1 9
A bag contains Rs 750 in the form of rupee, 50 P and 25 P coins in the ratio 5 : 8 : 4. Find the number of coins of each type.
S o l u t i o n :
Let the numbers one rupee, fifty paise and twenty-five paise coins be 5x, 8x and 4x, respectively.
Total value of these coins = (5x ×
100
100
+ 8x ×
50
100
+ 4x ×
25
100
)
? 5x +
8x
2
+
4x
4
=
20x + 16x + 4x
4
=
40x
4
= 10x
However, the total value is Rs 750.
? 750 = 10x
? x = 75
Hence, number of one rupee coins = 5 ×
75 = 375
Number of fifty paise coins = 8 ×
75 = 600
Number of twenty-five paise coins = 4 ×
75 = 300
Q u e s t i o n : 2 0
If (4x + 5) : (3x + 11) = 13 : 17, find the value of x.
S o l u t i o n :
(4x + 5) : (3x + 11) = 13 : 17
?
4x+ 5
3x + 11
=
13
17
? 68x + 85 = 39x + 143 ? 29x = 58 ? x = 2
Q u e s t i o n : 2 1
If x : y = 3 : 4, find (3x + 4y) : (5x + 6y).
S o l u t i o n :
x
y
=
3
4
? x =
3y
4
Now, we have (3x + 4y) : (5x + 6y)
=
3x +4y
5x + 6y
=
3×
3y
4
+4y
5×
3y
4
+6y
=
9y+16y
15y +24y
=
25y
39y
=
25
39
= 25 : 39
Q u e s t i o n : 2 2
If x : y = 6 : 11, find (8x - 3y) : (3x + 2y).
S o l u t i o n :
x
y
=
6
11
? x =
6y
11
Now, we have:
8x -3y
3x + 2y
=
8×
6y
11
-3y
3×
6y
11
+2y
=
48y-33y
18y + 22y
=
15y
40y
=
3
8
? (8x - 3y) : (3x + 2y) = 3 : 8
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FAQs on RS Aggarwal Solutions: Ratio and Proportion - Mathematics (Maths) Class 7
| 1. What is the definition of ratio and proportion? |  |
Ans. Ratio is the quantitative relationship between two or more quantities, indicating how many times one quantity is contained in another. Proportion is an equation that states that two ratios are equal.
| 2. How do I solve problems involving ratio and proportion? | |
Ans. To solve problems involving ratio and proportion, you can use the following steps:
1. Identify the given ratios or proportions.
2. Set up an equation using the given ratios or proportions.
3. Solve the equation to find the unknown value.
| 3. What are the different types of ratios? | |
Ans. There are four types of ratios:
1. Simple Ratio: It compares two quantities of the same kind.
2. Compound Ratio: It compares two or more simple ratios.
3. Duplicate Ratio: It compares the square of two quantities.
4. Sub-duplicate Ratio: It compares the square root of two quantities.
| 4. Can you give an example of solving a problem using ratio and proportion? | |
Ans. Sure! Let's solve the following problem:
If the ratio of boys to girls in a class is 3:5 and there are 24 boys, how many girls are there?
Solution:
Step 1: Given ratio of boys to girls = 3:5
Step 2: Let the number of girls be x.
According to the given ratio, we can set up the proportion:
3/5 = 24/x
Step 3: Cross-multiply and solve for x:
3x = 5 * 24
3x = 120
x = 40
Therefore, there are 40 girls in the class.
| 5. How can ratio and proportion be applied in real-life situations? | |
Ans. Ratio and proportion are used in various real-life situations, such as:
1. Cooking: Recipes often require ingredients to be used in a certain ratio or proportion.
2. Finance: Calculating interest rates, investments, and loan repayments often involve ratios and proportions.
3. Maps and Scales: Maps and scale models use ratios to represent real-life distances.
4. Mixing Solutions: Chemical solutions are often mixed in specific ratios and proportions for desired outcomes.
5. Sports and Fitness: Athletes and fitness enthusiasts use ratios and proportions to track progress and set goals.
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