Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 11 Ratio and Proportion Ex 11.2 Textbook Exercise Questions and Answers.
PSEB Solutions for Class 6 Maths Chapter 11 Ratio and Proportion Ex 11.2
1. Determine if the following are in proportion:
Question (i)
20, 40, 25, 50
Solution:
Yes,
Product of Extremes = 20 × 50 = 1000
Product of Means = 40 × 25 = 1000
∴ Product of Extremes = Product of Means
Hence, 20, 40, 25, 50 are in proportion.
Question (ii)
35, 49, 55, 78
Solution:
No,
Product of Extremes = 35 × 78 = 2730
Product of Means = 49 × 55 = 2695
∴ Product of Extremes ≠ Product of Means
Hence, 35, 49, 55, 78 are not in proportion
Question (iii)
24, 30, 36, 45
Solution:
Yes,
Product of Extremes = 24 × 45 = 1080
Product of Means = 30 × 36 = 1080
Since Product of Extremes = Product of Means
Hence, 24, 30,36,45 are in proportion
Question (iv)
10, 22, 45, 99
Solution:
Yes,
Product of Extremes = 10 × 99 = 990
Product of Means = 22 × 45 = 990
∴ Product of Extremes = Product of Means
Hence, 10,22,45,99 are in proportion
Question (v)
32, 48, 70, 210.
Solution:
No,
Product of Extremes = 32 × 210 = 6720
Product of Means = 48 × 70 = 3360
Since Product of Extremes ≠ Product of Means
Hence, 32, 48, 70, 210 are not in proportion.
2. Do the following ratios forms a proportion:
Question (i)
5:9 and 20 : 36
Solution:
Yes,
Product of Extremes = 5 × 36 = 180
Product of Means = 9 × 20 = 180
Since Product of Extremes = Product of Means
Hence, 5 : 9 and 20 : 36 are in proportion
Question (ii)
24 : 36 and 32 : 48
Solution:
Yes,
First ratio = 24 : 36 (Dividing both terms by 12) = 2 : 3
Second ratio = 32 : 48 (Dividing both terms by 16) = 2 : 3
∴ Both ratios are equal.
Hence, 24 : 36 and 32 : 48 are in proportion
Question (iii)
32 : 40 and 36 : 42
Solution:
No,
First ratio = 32 : 40 (Dividing both terms by 8) = 4 : 5
Second ratio = 36 : 42 (Dividing both terms by 6) = 6 : 7
∴ Both ratios are not equal.
Hence, 32 : 40 and 36 : 42 are not in proportion
Question (iv)
27 : 18 and 3:2
Solution:
Yes,
First ratio = 27 : 18 (Dividing both terms by 9) = 3 : 2
Second ratio = 3 : 2
∴ Both ratios are equal.
Hence, 27 : 18 and 3 : 2 are in proportion
Question (v)
35 : 28 and 77 : 44.
Solution:
No,
First ratio = 35 : 28 (Dividing both terms by 7) = 5 : 4
Second ratio = 77 : 44 (Dividing both terms by 11) = 7 : 4
∴ Both ratios are not equal.
Hence, 35 : 28 and 77 : 44 are not in proportion.
3. State true or false of the following:
Question (i)
4 : 3 : : 36 : 37
Solution:
False,
Product of Extremes = 4 × 37 = 148
Product of Means = 3 × 36 = 108
∴ Product of Extremes ≠ Product of Means
Hence, it is false.
Question (ii)
16 : 4 : : 20 : 5
Solution:
True,
Product of Extremes = 16 × 5 = 80
Product of Means = 4 × 20 = 80
∴ Product of Extremes = Product of Means
Hence, it is true
Question (iii)
19 : 43 : : 8 : 21.
Solution:
False,
Product of Extremes = 19 × 21 = 399
Product of Means = 43 × 8 = 344
∴ Product of Extremes ≠ Product of Means
Hence, it is false.
4. Determine if the following ratios form a proportion:
Question (i)
40 cm : 1 m and ₹ 12 : ₹ 30
Solution:
Yes,
First ratio = 40 cm : 1 m
= 40 : 100
(Dividing both terms by 20) = 2:5
Second ratio = ₹ 12 : ₹ 30
= 12 : 30
(Dividing both terms by 6) = 2:5
∴ Both ratios are equal.
Hence, 40 cm : 1 m and ₹ 12 : ₹ 30 are in proportion.
Question (ii)
25 min : 1 hour and 40 km : 96 km
Solution:
Yes,
First ratio = 25 min : 1 hour
= 20 min : 60 min
= 25 : 60
(Dividing both terms by 5) = 5 : 12
Second ratio = 40 km : 96 km
= 40 : 96
(Dividing both terms by 8) = 5 : 12
∴ First ratio = Second ratio
Hence, 25 min : 1 hour and 40 km : 96 km are in proportion.
Question (iii)
₹ 4 : 35 paise and 8 kg : 9 kg.
Solution:
No,
First ratio = ₹ 4 : 35 paise
= 400 paise : 35 paise
= 400 : 35
(Dividing both terms by 5)
= 80 : 7
Second ratio = 8 kg : 9 kg
= 8 : 9
∴ First ratio ≠ Second ratio
Hence, ₹ 4 : 35 paise and 8 kg : 9 kg are not in proportion.
5. Find the value of ‘x’ in each case:
Question (i)
25 : x :: 15 : 6
Solution:
Since, given terms are in proportion
∴ Product of Extremes = Product of Means
⇒ 25 × 6 = x × 15
⇒ \(\frac{25 \times 6}{15}\) = x
⇒ x = 10
Question (ii)
28 : 49 :: x : 56
Solution:
28 : 49 : : x : 56
Since, given terms are in proportion
∴ Product of Extremes = Product of Means
⇒ 28 × 56 = 49 × x
⇒ \(\frac{28 \times 56}{49}\) = x
⇒ x = 32
Question (iii)
8 : 20 :: 10 : x.
Solution:
8 : 20 : : 10 : x
Since, given terms are in proportion
∴ Product of Extremes = Product of Means
⇒ 8 × x = 20 × 10
⇒ x = \(\frac{20 \times 10}{8}\)
⇒ x = 25
6. Check if the following terms are in continued proportion:
Question (i)
1, 4, 16
Solution:
For continued proportion, 1, 4, 16 can be written as 1, 4, 4, 16
∴ Product of Extremes = 1 × 16 = 16
Product of Means = 4 × 4 = 16
∴ Product of Extremes = Product of Means
Hence, 1, 4, 16 are in continued proportion
Question (ii)
3, 9, 27
Solution:
For continued proportion, 3, 9, 27 can be written as 3, 9, 9, 27
∴ Product of Extremes = 3 × 27 = 81
∴ Product of Means =9 × 9 = 81
∴ Product of Extremes = Product of Means
Hence, 3, 9, 27 are in continued proportion.
Question (iii)
5, 10, 20.
Solution:
For continued proportion, 5, 10, 20 can be written as 5, 10, 10, 20
∴ Product of Extremes = 5 × 20 = 100
∴ Product of Means = 10 × 10 = 100
∴ Product of Extremes = Product of Means
Hence, 5, 10, 20 are in continued proportion.