Question

What number when increased by \[25\% \] becomes \[150\]?

Answer 1

Hint:
Here, we will assume the number to be found to be a variable. Then we will increase it by \[25\% \] and equate this relation to \[150\]. Finally, we will solve this equation and find the unknown number.

Complete step by step solution:
It is given to us that a particular number, when increased by \[25\% \] becomes \[150\]. We have to find the number.
Let us denote it by a variable \[x\].
Now, when \[x\] is increased by \[25\% \], it becomes equal to \[150\].
This means that when \[25\% \] of \[x\] is added to \[x\], we get \[150\]. We know that to find the percentage of a particular quantity, we have to multiply the percentage to that quantity.
So, to find \[25\% \] of \[x\], we will multiply \[25\% \], so we get
\[25\% \] of \[x = \dfrac{{25}}{{100}} \times x\].
Now we will add \[25\% \] of \[x\] to \[x\] and equate it to 150.
\[x + \dfrac{{25}}{{100}} \times x = 150\]
We will now reduce the fraction.
By dividing the numerator and denominator by 25, we get
\[ \Rightarrow x + \dfrac{1}{4} \times x = 150\]
Low taking LCM on LHS, we get
\[ \Rightarrow \dfrac{{4x + x}}{4} = 150\]
Adding like terms in the numerator on the LHS, we get
\[ \Rightarrow \dfrac{{5x}}{4} = 150\]
Multiplying by 4 and dividing by 5 on both sides of the above equation, we get
\[ \Rightarrow \dfrac{{5x}}{4} \times \dfrac{4}{5} = 150 \times \dfrac{4}{5}\]
\[ \Rightarrow x = 120\]
Hence, we get the value of \[x\] as 120.

Therefore, the required number is 120.

Note:
It must be noted that if the difference between the new number and the original number is positive, then there is a percentage increase in the original number. On the other hand, if the difference is negative, then there is a percentage decrease in the original number. A percentage is also used in real life to denote a certain change in climate or marks of a student.