Question

If a exceeds b by x% , then which of the following is correct?
a.$a - b = \dfrac{x}{{100}}$
b.$b = a + 100x$
c.$a = \dfrac{{bx}}{{100 + x}}$
d.$a = b + \dfrac{{bx}}{{100}}$

Answer 1

Hint: We are given that a exceeds b by x% and we know that x% of a number is given by multiplying x by the number and dividing it by 100 and $a = b + x\% {\text{ }}of{\text{ }}b$ and simplifying we get the required answer.

Complete step-by-step answer:
We have two numbers a and b
We are given that a exceeds b by x%
That is , a takes the value of b plus x% of b
We know that x% of a number is given by multiplying x by the number and dividing it by 100
Therefore x% of b $ = \dfrac{x}{{100}}*b = \dfrac{{bx}}{{100}}$
We are given that a exceeds b by x%
$
   \Rightarrow a = b + x\% {\text{ }}of{\text{ }}b \\
   \Rightarrow a = b + \dfrac{{bx}}{{100}} \\
$
From this, we get that the correct option is d.

Note: A percentage is one way of writing a ratio; one can also write it as a fraction or decimal. There are ways to convert fractions to percentages or decimals to percentages.
Percent means out of one hundred. It is often shown with the symbol "%". It is used even if there are not a hundred items. The number is then scaled so it can be compared to one hundred.