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# 0.75 of a number is 1200. What is $\dfrac{5}{8}$ of that number?(a) 1000(b) 1060(c) 880(d) 8002

Last updated date: 22nd Jul 2024
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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.

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.