Question

If 35% of a number is 12 less than 50% of that number, then the number is;
(A). 40
(B). 50
(C). 60
(D). 80

Answer 1

Hint: First assume the required number as variable x. Our aim is to find the value of variable x. To use the condition, first find 35% of x in terms of x. Next, find 50% of x in terms of x. Now relate them by using the condition given. Now you get a relation with x on both sides of the equation. Now use this relationship and then find the coefficient of the variable on both sides of the equation. Subtract the term with a coefficient of variable pm right-hand side. Now similarly find the constant values on both sides of the equation. Subtract the constant value of the left-hand side on both sides of the equation. Now you get an equation with variable terms on the left-hand side and constant terms on the right-hand side. Now find the coefficient on both sides of the equation. Now you have only the variable with coefficient 1 on the left-hand side and some constant on the right-hand side. So, this constant will be your result.

Complete step-by-step solution -
Linear Polynomials:
If the degree of the polynomial is 1 then they are called linear polynomials. For example, $x + 1, x + 2, x + 3$.
Degree of Polynomial:
The highest power of the variable in a polynomial is called its degree. For example \[{{x}^{2}}+4x+2\] has degree of 2, x + 1: degree of 1, \[{{x}^{3}}+1\]: degree of 3, 2 is a polynomial of degree 0.
Let us assume the required number as x:
By general knowledge, we can say that a % of b = \[\dfrac{a\times b}{100}\].
So, by using this, we get 35 % of x as follows:
\[\Rightarrow \] 35 % of x \[=\dfrac{35x}{100}\]
So, by using the same formula, we can write 50 % of x as:
 \[\Rightarrow \] 50 % of x \[=\dfrac{50x}{100}\]
Given condition in the question can be written as:
35 % of the number is 12 less than 50 % of the same number.
In another form we can write it as (which gives same meaning):
50 % of the number is 12 more than 35 % of the same number.
By substituting both equations of x, we get the equation:
\[\Rightarrow \dfrac{35}{100}\times x=\dfrac{50}{100}\times x-12\]
So, by removing the multiplication sign, we can write the equation as:
\[\Rightarrow \dfrac{35x}{100}=\dfrac{50x}{100}-12\]
By taking the least common multiple on the right-hand side, we get:
\[\Rightarrow \dfrac{35x}{100}=\dfrac{50x-1200}{100}\]
By canceling the common term, we get it as:
\[\Rightarrow \]$35x = 50x – 1200 $
By subtracting the term 50x on both sides, we get it as:
\[\Rightarrow \] $35x – 50x = - 1200 $
By simplifying the equation above, we can write it as:
\[\Rightarrow \]$-15x = - 1200 $
By dividing with -15 into both sides, we get it as:
\[\Rightarrow x=\dfrac{-1200}{-15}\]
By simplifying we get the value of x as 80.
Therefore the value of x satisfies the given condition is 80.

Note: After canceling 100 students write 12, instead of 1200 which is wrong. Don’t forget to multiply terms with 100. An alternate method is to keep all the variable terms to the right-hand side and constants to the left-hand side anyways you get the same result. Whenever you apply an operation to the left-hand side, don’t forget to apply the same on the right-hand side if not you may lead to the wrong answer.