Answer

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**Hint:**This problem is based on ratio and proportion. Ratio gives the comparison of two quantities which are of the same unit. Whereas proportion refers to equality of two ratios. The ratio is said to be an expression whereas proportion is an equation which can be solved.

**Complete step-by-step solution:**

$\left( a \right)$ Given:

For every $2$ people who order egg prata we have $5$people who order plain prata.

Hence, for $1$ people who order egg prata we have $\dfrac{5}{2}$people who order plain prata.

Therefore, if $'a'$ people order egg prata $\left( {\dfrac{{5a}}{2}} \right)$ people will order plain prata.

$\left( b \right)$ For every $5$ people who order plain prata we have $2$ people who order egg prata

Hence, for $1$ people who order plain prata we have \[\left( {\dfrac{2}{5}} \right)\] people who order egg prata

Therefore, if $'b'$ people order plain prata \[\left( {\dfrac{{2b}}{5}} \right)\] people will order egg prata.

$\left( C \right)$ Given, total number of people in shop $ = c$

Let number of people who ordered egg prata $ = d$

We known that number of people who ordered plain prata $ = \left( {\dfrac{{5d}}{2}} \right)$

$ \Rightarrow \left( {\dfrac{{5d}}{2} + d} \right) = c$

$ \Rightarrow \left( {\dfrac{{5d + 2d}}{2}} \right) = c$

On simplifying, we get

$ \Rightarrow \left( {\dfrac{{7d}}{2}} \right) = c$

$ \Rightarrow 7d = 2c$

On Simplifying to get $d$

$ \Rightarrow d = \dfrac{{2c}}{7}$

**Therefore, Number of people who ordered egg prata $ = \dfrac{{2c}}{7}$.**

**Note:**The ratio should exist only between the quantities of the same kind. We need to consider significant order of terms. While comparing two things, the units should be similar and also the comparison of two ratios can be performed only when ratios are equivalent like the fractions.

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