Question

A number exceeds \[25\% \] of itself by 60. Then number is?

Answer 1

Hint: Here, we have to find the number. We will frame an equation using the given conditions. Then we will convert the given percentage into the fraction using the formula. We will subtract the like terms and solve the equation further to get the required value.

Formula Used:
Amount of quantity is given by \[x = \dfrac{P}{{100}} \times n\] where \[x,P,n\] are the amount of quantity, percentage and the total amount respectively.

Complete step-by-step answer:
Let \[x\] be the number.
We are given that a number exceeds \[25\% \] of itself by 60. Mathematically, we can express this as:
\[x = 25\% \]of \[{\rm{ }}x + 60\]
Now converting the percentage using the formula \[x = \dfrac{P}{{100}} \times n\], we get
\[ \Rightarrow x = \dfrac{{25}}{{100}} \times {\rm{ }}x + 60\]
Taking the like terms on one side of the equation, we get
\[ \Rightarrow x - \dfrac{{25}}{{100}} \times {\rm{ }}x = 60\]
Simplifying the terms, we get
\[ \Rightarrow x - \dfrac{1}{4} \times {\rm{ }}x = 60\]
On taking LCM, we get
\[ \Rightarrow \dfrac{{4x}}{4} - \dfrac{x}{4} = 60\]
By subtracting the like terms, we get
\[ \Rightarrow \dfrac{{4x - x}}{4} = 60\]
\[ \Rightarrow \dfrac{{3x}}{4} = 60\]
By cross multiplying, we get
\[ \Rightarrow 3x = 60 \times 4\]
\[ \Rightarrow 3x = 240\]
By dividing the terms, we get
\[ \Rightarrow x = \dfrac{{240}}{3}\]
\[ \Rightarrow x = 80\]
Therefore, the number is \[80\].

Note: We should know that the key words to frame a necessary equation with the given conditions. We are given the word “exceeds” which means greater than. So, a number is greater than \[25\% \] of a number. The difference between a number and \[25\% \] of a number is 60. Thus the equation formed is a linear equation in one variable. A linear equation is an equation which has the highest degree of variable as 1 and has only one solution. Here there is only one variable and the degree is one so the solution will also be one.