Question

If p is 30% more than q, then find value of \[\dfrac{{p + q}}{q}\]
A. \[2.3\]
B. \[3.3\]
C. \[4.3\]
D. None of these

Answer 1

Hint:
Here we use the concept of percentage which means the part of a complete value. Percentage is always denoted by the sign % and opens up by dividing the value by \[100\]
* When any variable is \[x\% \] of another variable, then first variable is \[\dfrac{x}{{100}}\]times of the other variable i.e. \[m\% \] of \[x\] \[ = (\dfrac{m}{{100}}) \times x\] i.e. \[{(\dfrac{m}{{100}})^{th}}\] part of \[x\]
* When the variable is \[x\% \] more than another variable, then first variable is \[(1 + \dfrac{x}{{100}})\]times of the other variable i.e. \[x\] is \[m\% \] more than \[y\] means \[x\] is more than \[y\] by \[m\% \] of \[y\]
i.e. \[x = y + m\% (y) = y + \dfrac{m}{{100}} \times y = (1 + \dfrac{m}{{100}})y\]
* Whenever there are more than or less than type of questions, always add or subtract on the opposite side of that value that is given to be more/less.

Complete step by step solution:
Given, \[p\]is 30% more than \[q\].
Find the value of \[p\] in terms of \[q\] by substituting 30 for \[x\] into the formula \[1 + \dfrac{x}{{100}}\].
\[p = \left( {1 + \dfrac{{30}}{{100}}} \right)q\]
Divide 30 by 100 inside the parentheses.
\[p = \left( {1 + 0.30} \right)q\]
Add the terms inside the parentheses to obtain the relation between \[p\] and \[q\].
\[p = 1.3q\]
Substitute \[1.3q\] for \[p\] into \[\dfrac{{p + q}}{q}\].
\[\dfrac{{1.3q + q}}{q}\]
Add like terms on the numerator.
\[\dfrac{{2.3q}}{q}\]
Factor out the common factor, that is \[q\] to obtain the result.
\[ = 2.3\]

Therefore, Option A is correct.

Note:
In these kinds of questions students are likely to make a mistake of adding \[30\% \] to \[p\] as it is given ‘more’ in the statement. Also percentage of any value is always less than or equal to the value because percentage is a part of the value so it can never be greater than the value.
Alternative method:
Assume, \[q = 100\] . Then, \[30\% \] of \[q\] is calculated as \[\dfrac{{30}}{{100}} \times q = \dfrac{{30}}{{100}} \times 100 = 30\] .
Therefore, \[p\] is \[30\% \] more than \[q\] means that when \[30\% \] of \[q\] is added to \[q\] then it becomes equal to \[p\] .
\[p = 30\% q + q\]
Substituting the value of \[30\% \] of \[q\].
\[p = 30 + 100 = 130\]
Then the value of \[\dfrac{{p + q}}{q} = \dfrac{{130 + 100}}{{100}} = \dfrac{{230}}{{100}} = 2.3\]