Question

How do you find the percent of increase or decrease original: 400 new: 552?

Answer 1

Hint: Here in this question, we have to find the decrease or increase rate of given original to the new number, where original is the older quantity or measure and new is the newer quantity or measure. In this question we have to find the percent of increase because new quantity is larger than original quantity, first we have to find the difference between the new and original number next we divide the difference by original and then multiply by 100 on simplification we get the required result.

Complete step-by-step solution:
The term “percentage Increase” refers to the comparison of the increase in the value of the subject variable over a period of time relative to its original value. The formula for percentage increase can be derived by deducting the new value of the variable from its original value, then divide the result by the original value and multiply by \[100\% \] to express it in terms of percentage. Mathematically, it is represented as,
\[\text{Percent increase} = \dfrac{{\left( {New\,\, Value - Original \,\,Value} \right)\;}}{{Original\,\, Value}} \times 100\]
Consider the given question
Original quantity is
Original: 400
Newer quantity is
New: 552
Substitute the values into the formula.
i.e., Percentage increase \[ = \dfrac{{\left( {{\text{552}}-{\text{400}}} \right)\;}}{{400}} \times 100\]
on simplification, we get
Percentage increase\[ = 38\% \]
or
Subtract the original value from the new value, then divide the result by the original value.
\[ \Rightarrow \,\,\dfrac{{152\;}}{{400}}\]
Multiply the result by 100. The answer is the percent increase
\[ \Rightarrow \,\,0.38 \times 100\]
On simplification, we get
\[ \Rightarrow \,38\% \]

Hence, the percent of increase of measures original: 400 new : 552 is \[38\% \].

Note: We have to know about the formula \[\text{Percent increase} = \dfrac{{\left( {New\,\, Value - Original \,\,Value} \right)\;}}{{Original \,\,Value}} \times 100\]

  by inserting the values to the formula we can determine the solution. We use simple arithmetic operations to solve the given problem. Here again we multiply the final answer with 100 to convert inot the percentage form.