Ncert solutions

Ncert solutions

Grade 6

Ratio and Proportion | Exercise 12.1

Question 15

Q1) 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

SOLUTION:

i) 15,45,40,120

we have 15,45,40,120

ratio of 15 to 45=\frac{15}{45}=\frac{15\div15}{45\div15}=\frac{1}{3}=1:3

[HCF OF 40 and 15, 45 is 15]

ratio of 40 to 120=\frac{40}{120}=\frac{40\div40}{120\div40}=\frac{1}{3}=1:3

[HCF of 40 and 120 is 40]

here, 15:4=40:120=1:3

ii) 33, 121,9,96

we have 33,121,9,96

ratio of 33 to121 = \frac{33}{121}=\frac{33\div11}{121\div11}=\frac{3}{11}

ratio of 9 and 96= \frac{9}{96}=\frac{9\div3}{96\div3}=\frac{3}{32}

[HCF of 9 and 96 is 3]

here, 3:11\ne3:32

i.e\ 33:121\ne9:96

therefore, 31,121,9 and 96 are not in proportion.

iii) 24,28,36,48

ratio of 24 and 28 is \frac{24}{28}=\frac{24\div4}{28\div4}=\frac{6}{7}=6:7

[HCF of 36 and 48 is 12]

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Question 15

Q1) 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

SOLUTION:

i) 15,45,40,120

we have 15,45,40,120

ratio of 15 to 45=\frac{15}{45}=\frac{15\div15}{45\div15}=\frac{1}{3}=1:3

[HCF OF 40 and 15, 45 is 15]

ratio of 40 to 120=\frac{40}{120}=\frac{40\div40}{120\div40}=\frac{1}{3}=1:3

[HCF of 40 and 120 is 40]

here, 15:4=40:120=1:3

ii) 33, 121,9,96

we have 33,121,9,96

ratio of 33 to121 = \frac{33}{121}=\frac{33\div11}{121\div11}=\frac{3}{11}

ratio of 9 and 96= \frac{9}{96}=\frac{9\div3}{96\div3}=\frac{3}{32}

[HCF of 9 and 96 is 3]

here, 3:11\ne3:32

i.e\ 33:121\ne9:96

therefore, 31,121,9 and 96 are not in proportion.

iii) 24,28,36,48

ratio of 24 and 28 is \frac{24}{28}=\frac{24\div4}{28\div4}=\frac{6}{7}=6:7

[HCF of 36 and 48 is 12]

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