Question

If $x\% $of $24 = 64,$then the value of x is ______
A.$37\dfrac{1}{2}$
B.$133\dfrac{1}{3}$
C.$266\dfrac{2}{3}$
D.$66\dfrac{2}{3}$

Answer 1

Hint: Here first of all understand the given data and convert the expression in the mathematical form and simplify using the percentage concept. Make the required term the subject by moving all the terms on the opposite side.

Complete step-by-step answer:
Take the given expression: $x\% $of $24 = 64$
Convert the given expression in the form of the mathematical expression and here “of” suggests the multiplication operator.
$x\% \times 24 = 64$
We know that percentage is always based on the number hundred. Percentage is the fraction where the denominator is always hundred.
$\dfrac{x}{{100}} \times 24 = 64$
Perform cross multiplication where the denominator of one side is multiplied with the numerator of the opposite side.
$x = \dfrac{{64 \times 100}}{{24}}$
Find the factors of the term in the numerator and the denominator –
$x = \dfrac{{8 \times 8 \times 100}}{{8 \times 3}}$
Common multiples from the numerator and the denominator cancel each other and therefore remove from the numerator and the denominator.
$x = \dfrac{{800}}{3}$
Now convert the above expression in the form of the mixed fraction.
$x = 266\dfrac{2}{3}$
Hence, from the given multiple choices – the option C is the correct answer.
So, the correct answer is “Option C”.

Note: Mixed fraction can be expressed when the numerator of the fraction is greater than the denominator and it is the expression when the integer is expressed along with the fraction. Be good in finding the factors and remember the multiples till at least twenty. Always remember that the common factors from the numerator and the denominator cancels each other