Answer

Verified

390.3k+ views

**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 The amount withdrawn from the ATM is valued at \[Rs.25000\].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 \[125\].

Recently Updated Pages

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

10 examples of friction in our daily life

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Who was the first to raise the slogan Inquilab Zindabad class 8 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

One cusec is equal to how many liters class 8 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

A resolution declaring Purna Swaraj was passed in the class 8 social science CBSE