Question

Mr. Kapoor withdrew $Rs.25000$ from an ATM. If he receives 150 notes in denomination of Rs.$500$ and Rs.$100$. Find the number of notes in each denomination

Answer 1

Let us assume the $500$ and $100$ denomination notes as $x$ and $y$ after assuming the total number of notes and their monetary value equivalence we form two equations that is product of total money amounting from $500$ denomination added to that of the denomination amounting for $100$ rupees. After that we will equate the equations and then subtract to find the value of $x$ and then the
value of $y$.

Complete step by step solution:
As given in the question, the value of $500$ notes and $100$ notes total to be $150$ number of notes. The amount withdrawn from the ATM is valued at $Rs.25000$.
Hence, let us assume that the total number of $500$ notes are $x$. And assume that the total number of $100$ notes are $y$. Therefore, the sum of $500$ denomination and $100$ denomination notes are to written as:
$x\text{ }+\text{ }y\text{ }=\text{ }150$
The total amount of $500$ denomination amounts to Rs $500x$ and the total amount of $100$ denomination amounts to Rs. $100y$.
Hence adding the total amount will form an Equation of $500x+100y=25000$
Subtracting the Equation based on the two situations, we get the value of $y$ as:

x\text{ }+\text{ }y\text{ }=\text{ }150\text{ } \\\ 500x+100y=25000 \\\ \end{matrix}$$ Multiplying the base equation with the above equation we get the two equation as: $$\Rightarrow \begin{matrix} 500x+\text{500}y=75000\text{ } \\\ 500x+100y=25000\text{ } \\\ \end{matrix}$$ $$\Rightarrow \text{400}y=50000$$ $$\Rightarrow y=\dfrac{50000}{400}$$ $$\Rightarrow y=125$$ And after getting the value of $$y$$ we put the value in the equation to get the value of $$x$$ by placing the value of $$y$$ in the equation $$x\text{ }+\text{ }y\text{ }=\text{ }150$$, we get the value of $$x$$ as: $$\Rightarrow x\text{ }+\text{ }125\text{ }=\text{ }150$$ $$\Rightarrow x=25$$ **Therefore, the total number of $$500$$ denominations is given as and the number of \100\ denomination is given as $$25$$ and $$125$$ respectively.** **Note:** Another method to find the number of notes is that we assume that the denomination of $$500$$ notes as $$x$$ and the number of $$100$$ denominations as $$150-x$$. Hence, the equation for the total sum and the number of denomination is: $$\Rightarrow 500x+100\left( 150-x \right)=Rs.25000$$ $$\Rightarrow 500x+15000-100x=Rs.25000$$ $$\Rightarrow 400x=Rs.\left( 25000-15000 \right)$$ $$\Rightarrow x=\dfrac{Rs.\left( 25000-15000 \right)}{400}$$ $$\Rightarrow x=\dfrac{Rs.10000}{400}$$ $$\Rightarrow x=25$$ Therefore, the number of $$500$$ notes as $$25$$ and $$100$$ notes as $$125$$.