Question

By what percent is B’s weight more than that of A , if A’s weight is $25\% $ less than that of B?

Answer 1

Hint:
Assuming the total weight to be 100. And by using the property that a% of a number b is given by $\dfrac{a}{{100}}\times b$ we get the value of A and B and with this we need to find $\dfrac{{B - A}}{A}$ to get the required value.

Complete step by step solution:
As we are given in percentage we can assume the total weight to be 100
We are given that the weight of A is $25\% $less than that of B
That is $\left( {100 - 25} \right)\% $of B $ = 75\% $ of B
We know that a% of a number b is given by $\dfrac{a}{{100}}\times b$
$ \Rightarrow A = \dfrac{{75}}{{100}}B$ ……(1)
From this we get
$ \Rightarrow B = \dfrac{{100}}{{75}}A$…….(2)
In order to find the percent by which B is more than A we need to find $\dfrac{{B - A}}{A}$
This ratio gives the required percentage
Lets subtract (1) from (2)
$ \Rightarrow B - A = \dfrac{{100}}{{75}}A - \dfrac{{75}}{{100}}B$………(3)
Now lets substitute the value of B from (2)
$
   \Rightarrow B - A = \dfrac{{100}}{{75}}A - \dfrac{{75}}{{100}}\times \dfrac{{100}}{{75}}A \\
   \Rightarrow B - A = \dfrac{{100}}{{75}}A - A \\
   \Rightarrow B - A = \dfrac{{100A - 75A}}{{75}} = \dfrac{{25A}}{{75}} \\
   \Rightarrow \dfrac{{B - A}}{A} = \dfrac{1}{3} \\
 $
Now to convert $\dfrac{1}{3}$into percentage we need to multiply this by 100
The required percentage is $\dfrac{1}{3}\times 100 = 33.33\% $

Hence we get that B is 33.33% more than A.

Note:
If we are given that A is more than B and asked for what percentage A is more than B then it is given by the ratio $\dfrac{{A - B}}{B}$
Percentages are one way of writing numbers; you can also write percentages as fractions or decimals.