Question

After an increase of 20% a number income 540. Find the original value.

Answer 1

Hint:
we know about the meaning of the percent. Percent means out of one hundred, for example: 20% is equal to $\dfrac{{20}}{{100}}$. Firstly, we consider the unknown original value as x and then consider the percent rate of the decrease or increase. Use the formula of increase or decrease.

Complete step by step solution:
The percentage increase in the values is 20%.
The income after the increased value is 540.
We can assume that the original value is x.
Now we can calculate the original value x from the formula of increase as given in the expression below.
${\text{Increase in 20 % }} = x + \dfrac{{20}}{{100}}x$
We can see that we know everything in the above expression apart from x. There is one unknown and one equation. It is known that it requires the n number of equations to evaluate n unknowns.
Thus, we can substitute the value of increase in 20% as 540 in the above formula.
${\rm{540}} = x + \dfrac{{20}}{{100}}x\\
\Rightarrow 540 = \left( {1 + \dfrac{1}{5}} \right)x\\
\Rightarrow 540 = \dfrac{6}{5}x\\
\Rightarrow x = 450$

Hence, the original value from the above result is 450.

Additional Information:
A lot of problems come up with the above formula. We can evaluate the increased amount or even the percentage increase from this formula. The percentage decrease formula is no different from this formula. Just a sign change is needed in the percentage decrease formula.

Note:
Here you should know the difference between increase and decrease formula. If the percent rate increases then use the formula ${\text{Increase in 20 % }} = x + \dfrac{{20}}{{100}}x$ and if the percent rate decreases then use the formula ${\text{Decrease in 20 % }} = x - \dfrac{{20}}{{100}}x$.