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# A number decreased from 80 to 50. By what percent of its original value has this number decreased? Write an answer in the form of the nearest integer greater than the answer.

Last updated date: 13th Jul 2024
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Hint: To find the percentage of decrease, we have to use the formula $\text{Percentage decrease}=\dfrac{\text{Decreased value}}{\text{Original value}}\times 100$ . Now, we have to find the decreased value by subtracting the new value from the original value. Here, we are given the original value as 80 and the new value as 50. Now, we have to substitute these values in the formula for percentage decrease. The final answer must be in the form of the nearest integer greater than the answer.

Complete step by step solution:
We are given that the number decreased from 80 to 50. We have to find the percentage of decrease. We know that the percentage of decrease is the decreased value divided by the original value and the result is multiplied by 100.
$\Rightarrow \text{Percentage decrease}=\dfrac{\text{Decreased value}}{\text{Original value}}\times 100...\left( i \right)$
We can find the decreased value by subtracting the new value from the original value.
$\text{Decreased value}=\text{Original value}-\text{New value}$
We are given that the original value is 80 and the new value is 50. Therefore, we can find the decreased value as
$\text{Decreased value}=80-50=30$
Now, we have to substitute this value in the equation (i).
$\Rightarrow \text{Percentage decrease}=\dfrac{30}{80}\times 100$
Let us cancel the zeroes from the numerator and the denominator.
$\Rightarrow \text{Percentage decrease}=\dfrac{3\require{cancel}\cancel{0}}{8\require{cancel}\cancel{0}}\times 100$
We can write the result of the above simplification as
$\Rightarrow \text{Percentage decrease}=\dfrac{3}{8}\times 100$
Now, we have to cancel the common factor of 4 from the denominator and the numerator.
$\Rightarrow \text{Percentage decrease}=\dfrac{3}{{{\require{cancel}\cancel{8}}^{2}}}\times {{\require{cancel}\cancel{100}}^{25}}$
We can write the result of the above simplification as
\begin{align} & \Rightarrow \text{Percentage decrease}=\dfrac{3}{2}\times 25 \\ & \Rightarrow \text{Percentage decrease}=\dfrac{75}{2}\% \\ \end{align}
We have to divide 75 by 2.
$\Rightarrow \text{Percentage decrease}=37.5\%$
We have to write the answer in the form of the nearest integer greater than 37.5%. Therefore, the required percentage = 38%.

Note: Students can get confused with the formulas of percentage increase and decrease. Percentage increase is given by $\text{Percentage increase}=\dfrac{\text{Increased value}}{\text{Original value}}\times 100$ , where increased value is obtained by subtracting the original value from the new value. Students should never forget to write the final answer in the form of the nearest integer greater than 37.5%.