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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

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Last updated date: 22nd Jul 2024
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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.