Question

A number A exceeds B by 25%. By what percentage is A more than B?
a. 20%
b. 25%
c. 30%
d. 15%

Answer 1

Hint: Given that number A exceeds B by 25% and we have to calculate the percentage by which A is more than B. 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.

Complete step-by-step answer:

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 $${\displaystyle \frac{25}{100}}$$ times of B.

Let, the number B be 100.
Then applying the situations given in the question we have,
Number A = B + $${\displaystyle \frac{25}{100}}$$(times of B)
$$\Rightarrow$$ Number A = B + $${\displaystyle \frac{25}{100}}$$ B

Substituting the value of B as assumed to be 100 we have,
Number A = 100+25
$$\Rightarrow$$number A = Rs.125.

Now we have to calculate by what percentage is A more than B.
To do so we first calculate the difference of A and B.
The difference is A – B = Rs. (125-100)
$$\Rightarrow$$ The difference is A – B = Rs. 25.

Now to calculate the value of percentage by which A more than B.
Or we calculate the value of percentage B which is less than A given by,

Percentage B less than A = $${\displaystyle \frac{25}{125}}(100\mathrm{\%})$$
Gives a percentage by which B less than A = 20%.
Thus, B is 20% less than A.
Therefore, the percentage by which A is more than B is 20%, which is option (a).

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.