Answer

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**Hint:**Firstly, we have to assume the number to be x. Then we have to find the value of x by forming and solving the equation obtained from the statement 0.75 of x is 1200. Then, we have to find the value of $\dfrac{5}{8}$ of x by writing the mathematical form of this expression and substituting the value of x in this expression.

**Complete step by step answer:**

Let us assume the number to be x. We are given that 0.75 of a number is 1200. We can write this in the form of algebraic expression as follows.

$\Rightarrow 0.75x=1200$

We have to find the value of x. For this, let us take the coefficient of x to the RHS.

$\Rightarrow x=\dfrac{1200}{0.75}$

We have to multiply and divide the RHS by 100.

$\begin{align}

& \Rightarrow x=\dfrac{1200}{0.75}\times \dfrac{100}{100} \\

& \Rightarrow x=\dfrac{120000}{75} \\

\end{align}$

We have to divide 120000 by 75.

$\Rightarrow x=1600$

Now, we have to find $\dfrac{5}{8}$ of x. We can write this statement mathematically as

$\Rightarrow \dfrac{5}{8}\times x$

Let us substitute the value of x in the above expression.

$\Rightarrow \dfrac{5}{8}\times 1600$

We can cancel the common factor from 1600 and 8.

$\begin{align}

& \Rightarrow \dfrac{5}{\require{cancel}\cancel{8}}\times {{\require{cancel}\cancel{1600}}^{200}} \\

& =5\times 200 \\

& =1000 \\

\end{align}$

Therefore, $\dfrac{5}{8}$ of x is 1000.

**So, the correct answer is “Option a”.**

**Note:**Students must be able to form algebraic expressions and equations from the given statements. They must always assume the unknown quantity as a variable. In algebra, ‘of’ and ‘times’ means ‘multiply’ or we replace these words by the multiplication sign ( $\times $ ). Students must understand the concept of algebra, rules involved in it and must be able to solve algebraic expressions and equations.

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