Question

A number A exceeds B by 25\% \]. By what percent is B short of A?
1. \[20\% \]
2. \[25\% \]
3. \[30\% \]
4. None

Answer 1

Hint: Given that number A exceeds B by \[25\% \] and we have to calculate the percentage by which B is short of A. To solve this type of question we always assume one of the given two numbers as \[100\] and then proceed according to given conditions of the question to obtain the answer as we first find the $25\% of B $ then find the value of A with the help of this and solve further using percentage.

Complete step-by-step solution:
The percentage means, a part per hundred. The percentages have no dimension. Hence it is called a dimensionless number. Percentages can also be represented in decimal form or fraction form.
Given a number A exceeds B by \[25\% \] means A is \[25\% \] more than B.
Converting the above percentage into the number we have A is equal to B adding to \[\dfrac{{25}}{{100}}\] times of B.
Let the number B be \[100\].
Then applying the situations given in the question we have, Number A \[ = B + \dfrac{{25}}{{100}} \times B\]
Substituting the value of B as assumed to be \[100\] we have,
Number A \[ = 100 + 25\]
\[ = 125\]
Now we have to calculate by what percentage is B short of A.
To do so we first calculate the difference of A and B.
The difference is \[A - B = 25\]
Now to calculate the value of percentage by which B is short of A.
Percentage B less than A \[ = \dfrac{{25}}{{125}} \times 100 = 20\% \]
Thus B is short of A by \[20\% \].
Therefore option (1) is the correct answer.

Note: The possibility of error in the question is assuming the wrong number between A and B as \[100\] and then using the given conditions of the question which will obviously result in an incorrect solution. The percentages have no dimension. Hence it is called a dimensionless number.