\({2\over7}=({2\over7}\times100)\%={200\over7}\%=28{4\over7}\%\)

\({5\over4}=({5\over4}\times100)\%=(5\times25)\%=125\%\)

144 cows

Rs840

Let the mean proportion between 4 and 64 be x.
So, 4:x::x:64 \(\Rightarrow {4\over x}={x\over64}\Rightarrow x \times x=64\times 4 \Rightarrow x^2=256 \Rightarrow x^2=16\times16\)
x=16                                      [\(\because \) product ofmeans = product of extremes]   
Hence, the mean proportion between 4 and 64 is 16          

Yes,such type of examples are as follows:
(i) In class VII, a test of Maths of 100 marks was conducted and observation was as follows:
20% students got marks below 50. 36% students got marks between 60 and 75. 44% students got marks
above 80.
(ii) An alloy is made up of the following composition: i.e. 35% copper, 43% nickel and 22% zinc

According to the question, if there are 100 fruits in a basket, out of them 50 are apples and 30 are oranges, then remaining would be mangoes.
Now, mangoes = 100 - (50 + 30)
= 100 - 80 = 20
Hence, there are 20% mangoes in the basket.

Putting the data in the tabular form, we get

We have, 30 days to 36 h
We know that,
1 day = 24 h \(\Rightarrow\)30 days = 24 X 30 h = 720 h
\(\therefore\) Required ratio = 30 days: 36 h = 720 h : 36 h
\(=720:36={760\over36}={80\over4}\\ ={20\over1}or 20:1\)

We have, Rs  5 to 50 paise
We know that, Rs 1= 100 paise = 5 x 100 paise = 500 paise
\(\therefore\) Required ratio = Rs 5: 50 paise = 500 paise: 50 paise
=500:50=\({500\over50}={50\over5}={10\over1}or10:1\)

(i) Given, ratio of calcium, carbon and oxygen in a chalk stick are 10: 3: 12.
Sum of the parts = 10 + 3 + 12 = 25
\(\therefore\)Percentage of carbon in chalk stick 
\(=\left({Part \ of \ carbon \ in \ chalk \ stick \over Total \ part \ of \ chalk}\times100\right)\%\)
\(=\left({3\over25}\times100\right)\%=(3\times4)\%=12\%\)
Hence, the percentage of carbon in a chalk stick is 12%.
(ii) Let the weight of the chalk stick be x g.
Now, weight of carbon = 3 g (which is 12% of chalk)
\(\therefore\) 12% of  \( x =3 \Rightarrow {12\over100}\times x=3\)
\(\Rightarrow x={3\times100 \over12}=25g\)
Hence, the weight of the chalk stick is 25 g.

Here, 64% means that 64 parts out of 100 pans and
20% means 20 pans out of 100 parts.
Then, remaining pans = 100 - (64 + 20)
= 100 - 84 = 16 or 16%
Hence, 64% + 20% + 16% = 100%