Question

What is the percentage decrease, if a number reduces from 70 to 42?

Answer 1

Hint: To solve this problem, we must calculate the change in the number by subtracting the new value from the original value. Then, we can find the percentage change by using the formula
Percentage decrease = $\dfrac{\text{Decrease}}{\text{Original value}}\times 100\%$.

Complete step by step answer:
Let us assume the original number to be ${{x}_{1}}$ and the new number to be ${{x}_{2}}$ . So, the values of these variables are
$\begin{align}
  & {{x}_{1}}=70 \\
 & {{x}_{2}}=42 \\
\end{align}$
We need to calculate the percentage decrease.
We know that the formula to calculate percentage change is
Percentage change = $\dfrac{\text{Change}}{\text{Original value}}\times 100\%$
We can tweak this formula for calculation of percentage decrease,
Percentage decrease = $\dfrac{\text{Decrease}}{\text{Original value}}\times 100\%$
Here, the number id decreased from 70 to 42. Hence, we can easily calculate the Decrease in value.
Decrease = ${{x}_{1}}-{{x}_{2}}$
We can now substitute the values for ${{x}_{1}}\text{ and }{{x}_{2}}$, to get
Decrease = 70 – 42
Hence, the value of Decrease is
Decrease = 28
Here in this question, the original value is ${{x}_{1}}$ .
Thus, the Original value = 70.
Hence, the percentage decrease could be calculated as
Percentage Decrease = $\dfrac{28}{70}\times 100\%$
We can cancel the terms from numerator and denominator,
Percentage Decrease = $\dfrac{4}{10}\times 100\%$
Thus, Percentage Decrease = 40%.

Hence, the percentage decrease when a number is decreased from 70 to 42 is 40%.

Note: We can also solve the above problem by using the fact that 42 is 60% of 70. Thus, the decrease in value is (100 – 60) %, i.e., 40%. We must note that the denominator in percentage change is the original value, and not new value. So, we have 70 in the denominator.