Question

Simplify: $16\dfrac{2}{3}\% $ of $600\,gm$ $ - $$33\dfrac{1}{3}\% $ of $180\,gm$
A. $20\,gm$
B. $30\,gm$
C. $40\,gm$
D. $60\,gm$

Answer 1

Hint: In this question we have an expression where we have a mixed fraction i.e. $1\dfrac{1}{2}$ this type of fraction is called a mixed fraction. So we will first break the mixed fraction into a simpler fraction and then we will simplify it. Here we have been given a mathematical expression with the term “of” which means multiplication. So we apply this and solve the problem.

Complete step by step answer:
Here we have :
$16\dfrac{2}{3}\% $ of $600gm$ $ - $$33\dfrac{1}{3}\% $ of $180gm$
First we will take the first part i.e.
$16\dfrac{2}{3}\% $ of $600gm$
We will break the mixed fraction
$16\dfrac{2}{3}\% = \dfrac{{16 \times 3 + 2}}{3}\% $
It can further be written as $\dfrac{{50}}{3}\% $.
We should keep in mind that “of” means to multiply i.e. $ \times $
Now we put the value and simplify the first part, it can be written as
$\dfrac{{50}}{3} \times \dfrac{1}{{100}} \times 600$
On simplifying it gives the value
$50 \times 2 = 100$.

Now we will solve the second part :
$33\dfrac{1}{3}\% $ of $180gm$
Again we will break the mixed fraction first:
$33\dfrac{1}{3}\% = \dfrac{{33 \times 3 + 1}}{3}\% $
It can further be written as $\dfrac{{100}}{3}\% $.
Now we put this value and simplify the second part, it can be written as
$\dfrac{{100}}{3} \times \dfrac{1}{{100}} \times 180$
On simplifying it gives the value
$\dfrac{{180}}{3} = 60$.
Now by putting the value of both the parts, we can write the original expression as
$100 - 60 = 40gm$.

Hence the correct option is C.

Note:We should keep in mind that for problems like this, it is good to break up the information and visualize how it fits in together. We can write $\% $ as $\dfrac{1}{{100}}$.We should know that the above given expression is a mathematical expression. It should be noted that a mathematical expression does not involve any equal sign as it is an expression.We equal signs $\left( = \right)$ in mathematical equations not in expressions.