Question

Meena went to a bank to withdraw $\mathrm{Rs}.2000$. She asked the cashier to give her $\mathrm{Rs}.50$ and $\mathrm{Rs}.100$ notes only. Meena got $25$notes in all. Find how many notes of $\mathrm{Rs}.50$ and $\mathrm{Rs}.100$ she received.

Answer 1

Step 1. Form the linear equation according to the given information.

Given that the Meena withdraws $\mathrm{Rs}.2000$.

Consider that the number of $\mathrm{Rs}.50$ notes is $x$and,

The number of $\mathrm{Rs}.100$ notes is $y$

And total number of notes are $25$.

Therefore,

$\begin{array}{rcl}x+y& =& 25...\left(1\right)\\ 50x+100y& =& 2000...\left(2\right)\end{array}$

Step 2. Solve the obtained equation.

Multiply equation $\left(1\right)$ with $50$:

$50x+50y=1250...\left(3\right)$

Subtract equations $\left(3\right)$ from $\left(2\right)$:

$$\begin{gathered} 50x+100y-(50x+50y)=2000-1250 \\ \Rightarrow 100y-50y=750 \\ \Rightarrow 50y=750 \\ \Rightarrow y=15 \end{gathered}$$

Substitute $y=15$in equation $\left(1\right)$to find $x$:

$$\begin{gathered} x+15=25 \\ \Rightarrow x=25-15 \\ \Rightarrow x=10 \end{gathered}$$

Hence Meena receives $x=10$ notes of $\mathrm{Rs}.50$

And $y=15$ notes of $\mathrm{Rs}.100$

Hence, she received $10$ notes of $\mathrm{Rs}.50$ and $15$ notes of $\mathrm{Rs}.100$.