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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

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Last updated date: 22nd Feb 2024
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IVSAT 2024
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 The amount withdrawn from the ATM is valued at \[Rs.25000\].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 \[125\].