Question

If ‘A‘ is \[125\% \] of ‘B‘, then what percent of ‘A‘ is ‘B‘ will be?
(a) $0.75$
(b) $0.80$
(c) $0.18$
(d) None of these

Answer 1

Hint: The given problem revolves around the concepts of calculations of percentage. As a result, dividing the given value (in percentage) by $100$ with respect to the given number or value and then taking reciprocal on both sides, to get the desired value.

Complete step-by-step solution:
Since, we have given that,
A is \[125\% \] of B
As a result, we can mathematically we can expressed as
${\text{A}} = \dfrac{{125}}{{100}} \times {\text{B}}$
Multiplying and dividing the equation by $25$ so as to get the exact value (also, known as “simplest method“), we get
${\text{A}} = \dfrac{5}{4} \times {\text{B}}$
Solving the equation more exactly (if possible solving the equation till the decimal value or places), we get
\[{\text{A}} = \left( {1.25} \right) \times {\text{B}}\] … (i)
Hence, this is the value (or, percentage) with respect to ‘B‘ particularly.
Similarly,
To find the value (or, percentage) with respect to ‘A‘,
So,
Taking reciprocal on both the sides (that is, the multiplicative inverse of the respective term $\dfrac{1}{x} = {x^{ - 1}}$ where, ‘$x$’ is any number), we get
Hence, the equation (i) becomes
\[\dfrac{1}{{1.25}} \times {\text{A}} = {\text{B}}\]
Solving the equation mathematically, we get
\[0.80 \times {\text{A}} = {\text{B}}\]
Above equation can also be written as,
\[{\text{B}} = 0.80 \times {\text{A}}\]
Since, the value $0.80$ is ordinary,
So, in terms of percentage, multiplying it by $100$, we get
\[{\text{B}} = \left( {0.80 \times {\text{100}}} \right){\text{A}}\]
\[{\text{B}} = 80 \times {\text{A}}\]
$ \Rightarrow $B is \[80\% \] of A.
$\therefore \Rightarrow $ The option (b) is correct.

Note: One must be able to know the basic mathematics such as solving the algebraic equations by adding, subtracting, multiplication, dividing, etc. which seems to be efficient to solve real life problems (applications). Remember when the term percentage comes, divide the respective (given) value by $100$, i.e. $\% = \dfrac{1}{{100}}$ asked in the question, so as to be sure of our final answer.