We have,10 g:40 g \(=\frac{10}{40}=1:4\)
and 25 kg: 100 kg \(=\frac{25}{100}=1:4\)
So, they are in proportion.

Required area to yield 360 quintals wheat = 8 hectares of land
\(\therefore\) To yield 1 quintal wheat, required area \(=\frac{8}{360}\) hectares
\(\therefore\) To yield 540 quintals wheat, required area \(=540\times\frac{8}{360}\) hectares \(\frac{3\times8}{2}\) hectares = 12 hectares of land.

33,44,75 and 100 are in proportion.

Ratio=2:3

Given that, number of boys = 40 and number of girls = 80
Ratio of number of boys to the number of girls \(=\frac{Number\ of\ boys}{Number\ of\ girls}=\frac{40}{80}=\frac{1}{2}=1:2\)
 

1. \(\because\) Cost of 2 handkerchiefs = Rs. 30
\(\therefore\) Cost of 1 handkerchief = Rs. \(\frac { 30 }{ 2 } \) = 15
2. \(\because\) Cost of 3 kg rice = Rs. 600
\(\therefore\) cost of 1 kg rice = Rs. \(\frac { 600 }{ 3 } \)=200
3. \(\because\) Cost of 5 combs = Rs. 30
\(\therefore\) Cost of 1 comb = Rs. \(\frac { 30 }{ 5 } \) = Rs. 6
4. \(\because\) Cost of 12 envelopes = Rs. 60
\(\therefore\) Cost of 1 envelope = Rs. \(\frac { 60 }{ 12 } \) = Rs. 5
5. \(\because\) Cost of 8 postcards = Rs. 8
\(\therefore\)Cost of 1 postcard = Rs. \(\frac { 8 }{ 8 } \) ​​​​​​​= Rs. 1

14 : 19

(a) \(2:3=\frac{2}{3}\ and\ 4:5=\frac{4}{5}\)
2: 3 and 4: 5 are not equal, therefore ratios are not in proportion.
(b) \(25 g:200g=\frac{25}{200}=\frac{1}{8}=1:8\)
\(6kg:48kg=\frac{6}{48}=\frac{1}{8}=1:8\)
Hence, they form a proportion.
(c) \(440m:2km=\frac{440}{2000}[\because1\ km=1000\ m]\)
\(=\frac{11}{50}=11:50\)
\(55\ cm:3 m=\frac{55}{300}=\frac{11}{60}=11:60\)
So, they are not in proportion.
(d) \(200 mL:2.5 L=\frac{200}{2500}=\frac{2}{25}=2:25\)
\(Rs.4:Rs.50=\frac{4}{50}=\frac{2}{25}=2:25\)
So, they are in proportion.

(a) Here, 25 cm : 1 m = 25 cm : 1 x 100 cm [\(\because\)1 m=100em]
= 25 cm: 100 cm
\(=25:100=\frac{25}{100}=\frac{25\div25}{100\div25}=\frac{1}{4}=1:4\)
[dividing numerator and denominator both by 25]
and Rs.40:Rs.160=40:160=\(\frac{40}{160}=\frac{4}{16}=\frac{1}{4}=1:4\)
[dividing numerator and denominator both by 10]
Here, 1: 4 = 1: 4 i.e. 25 cm : 1 m = Rs.40 : Rs.160
So, the ratios of 25 cm : 1 m and Rs.40 : Rs.160 are in proportion.
i.e. 25 cm : 1 m: : Rs.40 : Rs.160
Now, middle terms are 1 m and Rs.40 and extreme terms are 25 cm and Rs.160.
(b) Here,39L:65L=39:65=\(\frac{39}{65}\)
\(=\frac{39\div13}{65\div13}\) [\(\because\) HCF of 39 and 65 = 13]
\(=\frac{3}{5}=3:5\)
and 6 bottles: 10 bottles = 6 :10 \(=\frac{6}{10}\)
\(=\frac{6\div2}{10\div2}=\frac{3}{5}=3:5\)
[dividing numerator and denominator both by 2]
Here, 3 : 5 = 3 :5 i.e. 39 L : 65 L = 6 bottles: 10 bottles.
So, the ratio of 39 L : 65 Land 6 bottles: 10 bottles are in proportion.
i.e. 39 L : 65 L : : 6 bottles: 10 bottles
Now, middle terms of ratios are 65 Land 6 bottles and extreme terms of ratios are 39 Land 10 bottles.
(c) Here, 2kg:80kg=2:80=\(=\frac{2}{80}=\frac{2\div2}{80\div2}=\frac{1}{40}=1:40\)
[dividing numerator and denominator both by 2]
and 25 g : 625 g = 25 :625 \(=\frac{25}{625}=\frac{25\div25}{625\div25}=\frac{1}{25}=1:25\)
[\(\because\)HCF of 25 and 625 = 5 X 5 = 25]
Since, both ratios are not equal.
\(\therefore\) 2 kg : 80 kg \(\ne\) 25 g : 625 g
Hence, the given ratios are not in proportion.
(d) Here, 200mL:2.5L=200 \(\times\frac{1}{1000}L:2.5\ L\)
\([\because\ 1\ mL=\frac{1}{1000}L]\)
\(=\frac{200}{1000}L:2.5L=0.200L:2.5L\)
\(=0.200:2.5=\frac{0.200}{2.5}=\frac{2}{25}=2:25\)
[multiplying numerator and denominator both by 10]
and Rs.4:Rs.50=4:50=\(\frac{4}{50}=\frac{4\div2}{50\div2}=\frac{2}{25}=2:25\)
[dividing numerator and denominator both by 2]
Here, 2 : 25 = 2 : 25 i.e. 200 mL : 2.5 L = Rs. 4 : Rs.50
So, the ratios of 200 mL : 2.5 L and Rs. 4 : Rs. 50 are in proportion.
i.e. 200 mL : 2.5 L: : Rs.4 : Rs. 50
Now, middle terms of ratios are 2.5 L and Rs.4 and extreme terms of ratios are 200 mL and Rs.50.

Given, number of girls = 2300
and total number of students = 4320
\(\therefore\) Number of boys = Total number of students - N umber of girls
= 4320 - 2300 = 2020
(a) Ratio = 115: 216
(b) Ratio = 101: 115
(c) Ratio = 101: 216

In the given figure,
Number of triangles = 3; Number of squares = 2
Number of circles = 2
\(\therefore\) Total number of figures = 3 + 2 + 2 = 7
(a) Required ratio of number of triangles to the number of circles \(=\frac{Number\ of\ triangles}{Number\ of\ circles}=\frac{3}{2}=3:2\)
(b) Required ratio of number of squares to all the figure \(=\frac{Number\ of\ squares}{Total\ number\ of\ figures}=\frac{2}{7}=2:7\)
(c) Required ratio of number of circles to all the figure \(=\frac{Number\ of\ circles}{Total\ number\ of\ figures}=\frac{2}{7}=2:7\)

Runs made by Anish in 6 overs = 42
\(\therefore\) Runs made by Anish in 1 over \(=\frac{42}{6}=7\)
Runs made by Anup in 7 overs = 63
\(\therefore\) runs made by Anup in 1 over \(=\frac{63}{7}=9\)
\(\because\) 9>7
Hence, Anup made more runs per over.

Given, cost of 7 m of cloth = Rs. 294
\(\therefore\) Cost of 1 m of cloth \(=Rs.\frac{294}{7}=Rs.42\)
\(\therefore\) Cost of 5 m of cloth = Rs.42 X 5 = Rs. 210
Hence, the cost of 5 m of cloth is Rs. 210.

We have, 33,121,9,96
\(\therefore\) Ratio of 33 to 121 \(=\frac{33}{121}=\frac{33\div11}{120\div11}\) [\(\because\) HCF of33 and 121= 11]
\(=\frac{3}{11}=3:11\)
and ratio of9 to 96 = \(\frac{9}{96}=\frac{9\div3}{96\div3}\)
[\(\because\)HCF of 9 and 96 = 3]
\(=\frac{3}{32}=3:32\)
Here, 3 : 11 \(\ne\)3 : 32 i.e. 33: 121 \(\ne\)9: 96
Therefore, 33,121,9 and 96 are not in proportion.

Given, cost of 12 pens = Rs.180
\(\therefore\ Cost\ of\ 1\ pen=\frac{Total\ cost\ of\ pens}{Number\ of\ pens}=Rs.\frac{180}{12}=Rs.15\) [\(\because\)1 dozen = 12 units]
Also given, cost of 8 ball pens = Rs.56
\(\therefore\ Cost\ of\ 1\ ball\ pen=\frac{Total\ cost\ of\ ball\ pens}{Number\ of\ ball\ pens}=\frac{Rs.15}{Rs.7}=\frac{15}{7}=15:7\)

Here,we have to convert 1.5 h into min.
We know that, 1h=60 min
\(\therefore\) 1.5 h=1.5 \(\times\) 60 min=90 min
\(\therefore\ Required ratio=\frac{30\ min}{90\ min}=\frac{30}{90}\)
\(\because\) 30 = 2 X 3 X 5 and 90 = 2 X 3 X 5 X 3
\(\therefore\) HCF 30 and 90 = 2 X 3 X 5 = 30
\(Ratio=\frac{30\div30}{90\div30}=\frac{1}{3}=1:3\)

\(\frac { 10 }{ 150 } \times 750\) = 50

1 year = 12 months
4000x12 = 48000

\(\frac { 15 }{ 3 } \times 25\) = 50

4 : 7 = \(\frac { 4 }{ 7 } \)
5 : 9 = \(\frac { 5 }{ 9 } \)
\(\frac { 4 }{ 7 } \neq \frac { 5 }{ 9 } \)

2:3=20:30

12:8 = \(\frac { 12 }{ 8 } =\frac { 12\div 4 }{ 8\div 4 } =\frac { 3 }{ 2 } \)=3:2

\(\frac { 50 }{ 40 } =\frac { 5 }{ 4 } \)=5:4

80000=2x40000