Question

What number when increased by $$25\mathrm{\%}$$ becomes $$150$$?

Answer 1

Hint:
Here, we will assume the number to be found to be a variable. Then we will increase it by $$25\mathrm{\%}$$ 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 $$25\mathrm{\%}$$ becomes $$150$$. We have to find the number.
Let us denote it by a variable $$x$$.
Now, when $$x$$ is increased by $$25\mathrm{\%}$$, it becomes equal to $$150$$.
This means that when $$25\mathrm{\%}$$ 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 $$25\mathrm{\%}$$ of $$x$$, we will multiply $$25\mathrm{\%}$$, so we get
$$25\mathrm{\%}$$ of $$x={\displaystyle \frac{25}{100}}\times x$$.
Now we will add $$25\mathrm{\%}$$ of $$x$$ to $$x$$ and equate it to 150.
$$x+{\displaystyle \frac{25}{100}}\times x=150$$
We will now reduce the fraction.
By dividing the numerator and denominator by 25, we get
$$\Rightarrow x+{\displaystyle \frac{1}{4}}\times x=150$$
Low taking LCM on LHS, we get
$$\Rightarrow {\displaystyle \frac{4x+x}{4}}=150$$
Adding like terms in the numerator on the LHS, we get
$$\Rightarrow {\displaystyle \frac{5x}{4}}=150$$
Multiplying by 4 and dividing by 5 on both sides of the above equation, we get
$$\Rightarrow {\displaystyle \frac{5x}{4}}\times {\displaystyle \frac{4}{5}}=150\times {\displaystyle \frac{4}{5}}$$
$$\Rightarrow x=120$$
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.