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

Here, HCF of 20 and 35 is 5.
\(\therefore\frac{20}{35}=\frac{20\div5}{35\div5}=\frac{4}{7}=4:7\)

Ratio=14:9

20

Rs.2190

6 : 14

Sum of ratios = 5 + 3 = 8
Total contribution = Rs. 1000
\(\therefore\) Contribution made by one employee 
= \(\frac { 5 }{ 8 } \times 1000\) = Rs. 625
Contribution made by other employee​​​​​​​
= \(\frac { 3 }{ 8 } \times 1000\) ​​​​​​​= Rs. 375

Here, number of boys = 20 and number of girls = 40
\(\therefore\) Ratio of number of boys to the number of girls \(=\frac{Number\ of\ boys}{Number\ of\ girls}=\frac{20}{40}=\frac{2}{4}\)
[dividing numerator and denominator by 10]
\(=\frac{1}{2}=1:2\)
Hence, the required ratio is 1 : 2.

Here, time taken by Saurabh is in minutes and time taken by Sachin is in hours. So,we have to convert time taken by both into the same unit.
\(\therefore\) Time taken by Sachin = 1 h = 1 X 60 min = 60 min [\(\because\)1 h =60 min]
and time taken by Saurabh = 15 min
\(\therefore\) Ratio of time taken by Saurabh to the time taken by Sachin \(=\frac{Time\ taken\ by\ Saurabh}{Time\ taken\ by\ Sachin}=\frac{15}{60}=\frac{15\div15}{60\div15}=\frac{1}{4}=1:4\) [\(\because\) HCF of 15 and 60=15]
Hence, the required ratio is 1 : 4.

We have, 1: 5 and 3: 15
Here, \(3:15=\frac{3}{15}=\frac{3\div3}{15\div3}=\frac{1}{5}=1:5\) [dividing numerator and denominator both by 3]
i.e. 1 : 5 and 3 : 15 are in proportion.
Thus, the proper form is 1 : 5 :: 3: 15.

We have, 15 : 45 and 5 : 25
Here, \(15:45=\frac{15}{45}=\frac{15\div15}{45\div15}\)
[dividing numerator and denominator both by 15]
\(=\frac{1}{3}=1:3\ and\ 5:25=\frac{5}{25}=\frac{5\div5}{25\div5}=\frac{1}{5}=1:5\)
[dividing numerator and denominator both by 5]
Here, 15 : 45 \(\ne\)5 : 25
Thus, 15 : 45 and 5 : 25 are not in proportion.

Given, in last 30 days, temperature drop = 15 degree
\(\therefore\) In 1 day, temperature drop \(=\frac{15}{30}\) degree
\(=\frac{15\div15}{30\div15}=\frac{1}{2}degree[\because \ HCF\ of\ 15\ and\ 30=15]\)
\(\therefore\) In next 10 days, temperature drop
\(=\frac{1}{2}\times10\ degree=5\ degree\)
Hence, temperature dropped 5 degree in the next 10 days.

(i) \(\frac{2}{3}=2:3\ and\ \frac{4}{6}=2:3\) Hence, \(\frac{2}{3}\ and \frac{4}{6}\) are equal.
(ii) \(\frac{8}{4}=2:1\ and\frac{2}{1}=2:1\) Hence, \(\frac{8}{4}\ and\frac{2}{1}\) are equal.
(iii) \(\frac{4}{5}=4:5\ and\frac{12}{20}=\frac{3}{5}=3:5\) Hence,\(\frac{4}{5}\ and\frac{12}{20}\) are not equal.

Given, number of girls = 20 and number of boys = 15
\(\therefore\) Total number of students in the class = 20 +15 = 35
(a) Ratio of number of girls to the number of boys \(=\frac{Number\ of\ girls}{Number\ of\ boys}=\frac{20}{15}\)
\(=\frac{20\div5}{15\div5}=\frac{4}{3}=4:3\) [ \(\because\)HCFof 20 and 15=5]
(b) Ratio of number of girls to the total number of students in the class \(=\frac{Number\ of\ girls}{Total\ number\ of\ students}=\frac{20}{35}\)
\(=\frac{20\div5}{35\div5}=\frac{4}{7}\) [ \(\because\) HCF of 20 and 35 = 5]

Given, money earned by Seema = Rs. 150000
and money saved by Seema = Rs. 50000
(a) \(Required\ ratio=\frac{Money\ earned\ by\ Seema}{Money\ saved\ by\ Seema}\)
\(=\frac{Rs.150000}{Rs.50000}=\frac{15000\div50000}{50000\div50000}=\frac{3}{1}=3:1\)
(b) \(\because\) Money spend by Seema = Earned money - Saved money
= Rs.(150000 - 50000) = Rs.100000
\(\therefore\ Required\ ratio=\frac{Money\ saved\ by\ Seema}{Money\ spend\ by\ Seema}=Rs.\frac{50000}{100000}\)
\(=\frac{50000\div50000}{100000\div50000}=\frac{1}{2}=1:2\) [\(\because\) HCF of 50000 and 100000 = 50000]

(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.

Reena's earning = Rs. 90000
Reena's saving = Rs.30000
Ratio of earning to the saving \(=\frac{90000}{30000}=3:1\)
The value depict here is economic planning for future.

\(\frac { 20 }{ 30 } =\frac { 2 }{ 3 } \)= 2:3