Question

If \[40\] is subtracted from \[60\% \] of a number, the result is \[50\]. Find the number.

Answer 1

Hint: In mathematics, a percentage is a number or ratio that is represented as a fraction out of 100. It is represented by the symbol “%”. Now, to calculate the percentage of a number, we need to use a formula such as: P% of Number = Z where Z is the required percentage/ number. Here, we will assume X as a number which we need to find. And then according to the question and formula we will get an equation which we will solve to get the final output.

Complete step by step answer:
Given that,
If \[40\] is subtracted from \[60\% \] of the number and the result obtained is \[50\].
So, we need to find the number.
Let that number from which \[60\% \] gets subtracted be $X$.
Thus, according to the question,
If \[40\] is subtracted from \[60\% \] of X, then we get \[50\].
As per the given condition, the equation becomes,
\[60\% \,of \, X - 40 = 50\]
\[ \Rightarrow 60\% (X) - 40 = 50\]
We know that % means out of 100. i.e.
\[ \Rightarrow \dfrac{{60}}{{100}}X - 40 = 50\]
By using transposition, and moving the LHS term to RHS, we get,
\[ \Rightarrow \dfrac{{60}}{{100}}X = 50 + 40\]
Simplify the above equation, we will get,
\[ \Rightarrow \dfrac{6}{{10}}X = 90\]
\[ \Rightarrow 6X = 90(10)\]
Taking all the values in RHS and keep only the unknown term in LHS, we get,
\[ \Rightarrow X = \dfrac{{90 \times 10}}{6}\]
Simplify this above equation, we will get,
\[ \Rightarrow X = 15 \times 10\]
\[ \Rightarrow X = 150\]
Therefore, the required number is $150$.

Note:
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. Hence, the percentage means, a part per hundred. The word percent means per 100. If we have to calculate percent of a number, we have to divide the value by the total value and then multiply the resultant to 100 i.e. Percentage formula = (Value/Total value)×100. Example: If we say, 50% of a number, then it means 50 percent of its whole.