Question

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

Answer 1

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 ${\displaystyle \frac{5}{8}}$ 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.
$\Rightarrow x={\displaystyle \frac{1200}{0.75}}$
We have to multiply and divide the RHS by 100.
$\begin{array}{rl}& \Rightarrow x={\displaystyle \frac{1200}{0.75}}\times {\displaystyle \frac{100}{100}}\\ & \Rightarrow x={\displaystyle \frac{120000}{75}}\end{array}$
We have to divide 120000 by 75.
$\Rightarrow x=1600$
Now, we have to find ${\displaystyle \frac{5}{8}}$ of x. We can write this statement mathematically as
$\Rightarrow {\displaystyle \frac{5}{8}}\times x$
Let us substitute the value of x in the above expression.
$\Rightarrow {\displaystyle \frac{5}{8}}\times 1600$
We can cancel the common factor from 1600 and 8.
$\begin{array}{rl}& \Rightarrow {\displaystyle \frac{5}{\text{cancel}8}}\times {\text{cancel}1600}^{200}\\ & =5\times 200\\ & =1000\end{array}$
Therefore, ${\displaystyle \frac{5}{8}}$ 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.