NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion (Ex 12.2) Exercise 12.2

Students often find Mathematics intimidating. Mathematical concepts, formulas, theorems, and calculations appear challenging to them. Due to the purely conceptual nature of this subject, students must be able to grasp its concepts at a deep level. Ratio and Proportion is the topics of Chapter 12 in Class 6. The concepts and calculations in this chapter might be difficult for students at first. With practise and guidance, the concepts and calculations will eventually become easier for them. Ratio and Proportion in Class 6 Mathematics Chapter-12 covers Introduction, Ratio, Proportion, and Unitary Method. Numerous exercises and questions are not included in the chapter, but various complex concepts are described. This may make it difficult for students to grasp these concepts and do well in the chapter. For students to perform effectively in their examinations, Extramarks provides them with all the essential resources to make their learning experience comprehensive and effortless.

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NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion (Ex 12.2) Exercise 12.2

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Access NCERT Solutions for Class 6 Maths Chapter 12- Ratio and Proportion

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NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.2

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Q.1 Determine if 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

Ans.

(a) Ratio of 15 and 45 = 15:45
= 1:3
Ratio of 40 and 120 = 40:120
= 1:3
Since, 15:45 = 40:120
Therefore, 15, 45, 40 and 120 are in proportion.

(b) Ratio of 33 and 121= 33:121
= 3:11
Ratio of 9 and 96 = 9:96
= 3:32
since, 33:121 ≠ 9:96
Therefore, 33, 121, 9 and 96 are not in proportion.
(c) Ratio of 24 and 28 = 24:28
= 6:7
Ratio of 36 and 48 = 36:48
= 3:4
since, 24:28 ≠ 36:48
Therefore, 24, 28, 36 and 48 are not in proportion.

(d) Ratio of 32 and 48 = 32:48
= 2:3
Ratio of 70 and 210 = 70:210
= 1:3
since, 32:48 ≠ 70:210
Therefore, 32, 48, 70 and 210 are not in proportion.
(e) Ratio of 4 and 6 = 4:6
= 2:3
Ratio of 8 and 12 = 8:12
= 2:3
since, 4:6 = 8:12
Therefore, 4, 6, 8 and 12 are in proportion.
(f) Ratio of 33 and 44 = 33:44
= 3:4
Ratio of 75 and 100 = 75:100
= 3:4
since, 33:44 = 75:100
Therefore, 33, 44, 75 and 100 are in proportion.

Q.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

Ans.

(a)   Ratio of 16 and 24=1624=8×28×3=23        Ratio of 20 and 30=2030=10×210×3=23So,​      16:24::20:30Therefore, it is true.(b)     Ratio of 21 and 6=216=3×73×2=72        Ratio of 35 and 10=3510=5×75×2=72So,​      21:6::35:10Therefore, it is true.(c)   Ratio of 12 and 18=1218=6×26×3=23        Ratio of 28 and 12=2812=4×74×3=73So,​      12:18≠28:12Therefore, it is False.(d)         Ratio of 8 and 9=89        Ratio of 24 and 27=2427=3×83×9=89So,​           8:9=24:27Therefore, it is True.(e) Ratio of 5.2 and 3.9=5.23.9=1.3×41.3×3=43              Ratio of 3 and 4=34So,​   5.2:3.9≠3:4Therefore, it is False.(f) Ratio of 0.9 and 0.36=0.90.36   =0.9×10.9×4   =14             Ratio of 10 and 4=104   =2×52×2   =52So,​  0.9:0.36≠10:4Therefore, it is False.

Q.3 Are the following statements true?
(a) 40 persons: 200 persons = 15: 75
(b) 7.5 litres: 15 litres = 5 kg: 10 kg
(c) 99 kg: 45 kg = 44: 20
(d) 32 m: 64 m = 6 sec: 12 sec
(e) 45 km: 60 km = 12 hours: 15 hours

Ans.

(a) Ratio of 40 persons and 200 persons=40200=40×140×5=15    Ratio of 15 and 75=1575=15×115×5=15So, 40 persons:200 persons= 15: 75Therefore, the given statement is true.(b)              Ratio of 7.5 litres and 15 litres=7.515=7.5×17.5×2=12       Ratio of 5 kg and 10 kg=510=5×15×2=12So, 7.5 litres:15 litres=5 kg:10 kg.Therefore, the given statement is true.(c)      Ratio of 99 kg and 45 kg=9945=9×119×5=115    Ratio of 44 and 20=4420=4×114×5=115∴                   99 kg:45 kg= 44: 20.Therefore, the given statement is true.(d)      Ratio of 32 m and 64 m=3264=32×132×2=12              Ratio of 6 sec and 12 sec=612=6×16×2=12∴                   32 m:64 m=6  sec:12 sec.          Therefore, the given statement is true.(e)             Ratio of 45 km and 60 km=4560=3×154×15=34          Ratio of 12 hours and 15 hours=1215=3×43×5=45∴                 45 km:60 km≠12 hours:15 hours.Therefore, the given statement is false.

Q.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 40 : 160
(b) 39 litres : 65 litres and 6 bottles : 10 bottles
(c) 2 kg: 80 kg and 25 g: 625 g
(d) 200 ml : 2.5 litre and 4 : 50

Ans.

(a)   Ratio of 25 cm and 1 m=25100            =14  Ratio of 40 and 160=40160 =40×140×4 =14Here, 25 cm:1 m= 40: 160.So, 25 cm:1 m and 40: 160 are in proportion.Middle terms of the proportion are: 1m and 40.Extreme terms of the proportion are: 25 cm and 160.(b) Ratio of 39 litres and 65 litres=3965             =13×313×5             =35  Ratio of 6 bottles and 10 bottles=610            =2×35×5            =35Here, 39 litres:65 litres=6 bottles:10 bottles.So, 39 litres:65 litres::6 bottles:10 bottles are in proportion.Middle terms of the proportion are: 65 litres  and  6 bottles.Extreme terms of the proportion are: 39 litres and 10 bottles.(c)   Ratio of 2 kg and 80 kg=280             =140                   Ratio of 25 g and 625 g=25625            =25×125×25            =125Here, 2 kg:80 kg≠25 g:625 g.So, 2 kg:80 kg and  25 g:625 g are not in proportion.(d)       Ratio of 200 ml and 2.5 l=2002500    [∵1l=1000 ml]            =225                    Ratio of 4 and 50=450            =2×22×25            =225Here, 200 ml:2.5 l::4:50.So, 200 ml:2.5 l  and  4:50 are in proportion.Middle terms of the proportion are: 2.5 litres and 4.Extreme terms of the proportion are: 200 ml and 50.

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