Class 6 - Mathematics : Ratio and Proportion
Exercise : 12.2
Top Block 1
NCERT Solutions Class 6 Mathematics Ratio and Proportion Ex 12.2
Question∶1. Determine the following are in proportion∶
(a) 15, 45, 40, 120
(b) 33, 121, 9, 96
(c) 24, 28, 36, 48
(d) 32, 48, 70, 210
(e) 4, 6, 8, 12
(f) 33, 44, 75, 100
Answer:
(a) 15 ∶ 45 = 1∶ 3
40 ∶ 120 = 1∶ 3
Since 15 ∶ 45 = 40 ∶ 120
Therefore 15, 45, 40, 120 are in proportion.
(b) 33 ∶ 121 = 3∶ 11
9 ∶ 96 = 3∶ 32
Since 33 ∶ 121 ≠ 9 ∶ 96
Therefore, 33, 121, 9, 96 are not in proportion.
(c) 24 ∶ 28 = 6∶ 7
36 ∶ 48 = 3∶ 4
Since 24 ∶ 28 ≠ 36 ∶ 48
Therefore 24, 28, 36, 48 are not in proportion.
(d) 32 ∶ 48 = 2∶ 3
70 ∶ 210 = 1∶ 3
Since 32 ∶ 48 ≠ 70 ∶ 210
Therefore 32, 48, 70, 210 are not in proportion.
(e) 4 ∶ 6 = 2∶ 3
8 ∶ 12 = 2∶ 3
Since 4 ∶ 6 = 8 ∶ 12
Therefore 4, 6, 8, 12 are in proportion.
(f) 33 ∶ 44 = 3∶ 4
75 ∶ 100 = 3∶ 4
Since 33 ∶ 44 = 75 ∶ 100
Therefore 33, 44, 75, 100 are in ratio.
Question∶ 2. Write True (T) or False (F) against each of the following statements∶
(a) 16 ∶ 24 ∷ 20 ∶ 30
(b) 21 ∶ 6 ∷ 35 ∶ 10
(c) 12 ∶ 18 ∷ 28 ∶ 12
(d) 8 ∶ 9 ∷ 24 ∶ 27
(e) 5.2 ∶ 3.9 ∷ 3 ∶ 4
(f) 0.9 ∶ 0.36 ∷ 10 ∶ 4
Answer:
(a) 16 ∶ 24∷ 20 ∶ 30 ⇒⇒23=23
Hence, it is True.
(b) 21 ∶ 6 ∷ 35 ∶ 10 ⇒⇒72=72
Hence, it is True.
(c) 12 ∶ 18 ∷ 28 ∶ 12 ⇒⇒23≠73
Hence, it is False.
(d) 8 ∶ 9 ∷ 24 ∶ 27 ⇒⇒89=89
Hence, it is True.
(e) 5.2 ∶ 3.9 ∷ 3 ∶ 4 ⇒⇒43≠34
Hence, it is False.
(f) 0.9 ∶ 0.36 ∷ 10 ∶ 4 ⇒⇒52=52
Hence, it is True.
Mddle block 1
Question∶ 3.Are the following statements true∶
(a) 40 persons ∶ 200 persons = Rs. 15 ∶Rs. 75
(b) 7.5 liters∶ 15 liters = 5 kg = 10 kg
(c) 99 kg ∶ 45 kg = Rs. 44 ∶Rs. 20
(d) 32 m ∶ 64 m = 6 sec. ∶ 12 sec.
(e) 45 km ∶ 60 km = 12 hours ∶ 15 hours
Answer:
(a) 40 persons ∶ 200 persons = 1∶ 5
Rs. 15 ∶Rs. 75 = 1∶ 5
Since, 40 persons ∶ 200 persons = Rs. 15 ∶Rs. 75
Hence, the statement is true.
(b) 7.5 liters∶ 15 liters= 1∶ 2
5 kg ∶ 10 kg = 1∶ 2
Since, 7.5 liters∶ 15 liters = 5 kg ∶ 10 kg
Hence, the statement is true.
(c) 99 kg ∶ 45 kg = 11∶ 5
Rs. 44 ∶Rs. 20 = 11∶ 5
Since, 99 kg ∶ 45 kg = Rs. 44 ∶Rs. 20
Hence, the statement is true.
(d) 32 m ∶ 64 m = 1∶ 2
6 sec ∶ 12 sec = 1∶ 2
Since, 32 m ∶ 64 m = 6 sec ∶ 12 sec
Hence, the statement is true.
(e) 45 km ∶ 60 km = 3∶ 4
12 hours ∶ 15 hours = 4∶ 5
Since, 45 km ∶ 60 km ≠ 12 hours ∶ 15 hours
Hence, the statement is true.
Question∶ 4.Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion∶
(a) 25 cm ∶ 1 m and Rs. 40 ∶Rs. 160
(b) 39 liters∶ 65 liters and 6 bottles ∶ 10 bottles
(c) 2 kg ∶ 80 kg and 25 g ∶ 625 g
(d) 200 ml ∶ 2.5 ml and Rs. 4 ∶Rs. 50
Answer:
(a) 25 cm ∶ 1 m = 25 cm ∶ (1 x 100) cm = 25 cm ∶ 100 cm = 1∶ 4
Rs. 40 ∶Rs. 160 = 1∶ 4
Since the ratios are equal, therefore these are in proportion.
Middle terms = 1 m, Rs. 40 and Extreme terms = 25 cm, Rs. 160
(b) 39 liters∶ 65 liters =6 bottles ∶ 10 bottles = 3∶ 5
Since the ratios are equal, therefore these are in proportion.
Middle terms = 65 liters, 6 bottles and Extreme terms = 39 liters, 10 bottles
(c) 2 kg ∶ 80 kg = 1∶ 40
25 g ∶ 625 g = 1∶ 25
Since the ratios are not equal, therefore these are not in proportion.
(d) 200 ml ∶ 2.5 liters = 200 ml ∶ (25 x 1000) liters = 200 ml ∶ 2500 ml = 2∶ 25
Rs. 4 ∶Rs. 50 = 2∶ 25
Since the ratios are equal, therefore these are in proportion.
Middle terms = 2.5 liters, Rs. 4 and Extreme terms = 200 ml, Rs. 50
