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# 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

Last updated date: 22nd Feb 2024
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Answer
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Hint: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 The amount withdrawn from the ATM is valued at $Rs.25000$.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:
$\Rightarrow \begin{matrix} x\text{ }+\text{ }y\text{ }=\text{ }150\text{ } \\ 500x+100y=25000 \\ \end{matrix}$
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 $125$.