Question

If \[6\dfrac{1}{4}\% \] of a weight is \[0.25Kg\] . What is \[45\% \] of the weight ?

Answer 1

Hint: We have to find the value of the \[45\% \] of the weight when it is given that \[6\dfrac{1}{4}\% \] of a weight is \[0.25Kg\] . We solve this question using the concept of percentage . First we will find the percentage of the actual weight using the given condition of percentage of weight and then again using the concept of the percentage we will find the value of the \[45\% \] of the weight . This gives the value of the required weight .

Complete step-by-step answer:
Given :
let us consider that the actual weight is given as \[x\] .
Now , we will find the value of \[x\] using the given conditions .
We , also know that the percentage of a number is written as :
\[x\% {\text{ }}of{\text{ }}b = \dfrac{x}{{100}} \times b\]
Using this , we get the value of \[x\] as :
\[0.25 = 6\dfrac{1}{4}\% \] of \[x\]
Which can be written as :
\[0.25 = \dfrac{{6\dfrac{1}{4}}}{{100}} \times x\]
Also , we can write the expression as :
\[\dfrac{{25}}{{100}} = \dfrac{{\dfrac{{25}}{4}}}{{100}} \times x\]
Cancelling the terms , we can write the expression as :
\[25 = \dfrac{{25}}{4} \times x\]
On further simplifying , we get the value of \[x\] as :
\[x = 4Kg\]
Now , we have to find the value of \[45\% \] of weight \[x\] .
We can write the expression for the value of weight as :
\[weight = 45\% \] of \[x\]
Also , we can write the expression as :
\[weight = \dfrac{{45}}{{100}} \times x\]
Substituting the values , we get the expression as :
\[weight = \dfrac{{45}}{{100}} \times 4\]
On further solving , we get the value of weight as :
\[weight = 1.80Kg\]
So, the correct answer is “\[1.80Kg\]”.

Note: We wrote the value of the percentage \[6\dfrac{1}{4} = 6.25\] . As using the property of writing the percentage of fixed fraction into its real number form .
The mixed fraction can be written as :
\[6\dfrac{1}{4} = \dfrac{{6 \times 4 + 1}}{4}\]
\[6\dfrac{1}{4} = \dfrac{{25}}{4}\]
And on solving , we get
\[6\dfrac{1}{4} = 6.25\]