Question

I had \[Rs.200\] with me. I gave \[x\] to Vidhur and \[\dfrac{x}{4}\] to Sanjay and I am left with \[\dfrac{x}{4}\]. The amount I gave to Vidhur is?

Answer 1

Hint: In order to find the amount I gave to Vidhur, firstly we must calculate the total amount given to Vidhur and Sanjay and then add up the amount that I am left with to the amount I lent to Vidhur and Sanjay. After the total calculation, we will be obtaining an expression, we must be equating it to \[Rs.200\] as it was the total amount I had. Upon solving it, we will be obtaining the value of \[x\] and that would be the amount given to Vidhur as well as the required answer.

Complete step by step answer:
Now let us learn about linear equations. A linear equation can be expressed in the form of any number of variables as required. As the number of the variables increases, the name of the equation simply denotes it. The general equation of a linear equation in a single variable is \[ax+b=0\]. We can find the linear equation in three major ways. They are: point-slope form, standard form and slope-intercept form.
Now let us find the amount given to Vidhur.
We are given that,
Total amount\[=Rs.200\]
Amount given to Vidhur\[=x\]
Amount given to Sanjay\[=\dfrac{x}{4}\]
Now let us find the total amount given to both Vidhur and Sanjay. We get,
\[\Rightarrow x+\dfrac{x}{4}=\dfrac{5x}{4}\]
Now we will be adding the amount left to the total amount given because we know that, \[\text{total amount=expenditure+savings}\]
So now let us consider that amount given to both of them as expenditure and amount left as savings. According to this, now let us add up the savings i.e. the amount left.
\[\Rightarrow \dfrac{5x}{4}+\dfrac{x}{4}=\dfrac{6x}{4}=\dfrac{3x}{2}\]
\[\dfrac{3x}{2}\] is nothing but the total amount. The actual total amount is \[Rs.200\]. Now let us equate both of them to obtain the value of \[x\].
We get,
\[\begin{align}
  & \Rightarrow \dfrac{3x}{2}=200 \\
 & \Rightarrow 3x=400 \\
 & \Rightarrow x=133.3 \\
\end{align}\]
\[\therefore \] The amount given to Vidhur is \[Rs.133.3\]

Note: In this case, we have considered only one variable though there were two amounts because the amounts were given from the same amount, so we must be aware while assigning or considering the variables as this could be the most commonly committed error.