Question

Form the pair of linear equations in the following problem and find their solution (if they exist) by any algebraic method:

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

Answer 1

Step 1: Form the linear equations

Let us assume the number of $Rs.50$ notes be $A$ and the number of $Rs.100$ notes be $B$

According to the given information,

$A+B=25\dots \dots \dots \dots \dots \dots \dots \left(i\right)$

$50A+100B=2000$

$\Rightarrow A+2B=40\dots \dots \dots \dots \dots \dots \dots \dots \left(ii\right)$

Step 2: Find the solution

Subtracting the equation $\left(i\right)$ from the equation $\left(ii\right)$ we get,

$A+2B-A-B=40-25$

$\Rightarrow$ $B=15$

Substituting in the equation $\left(i\right)$ we get,

$A+15=25$

$\Rightarrow$ $A=10$

Hence, Meena has $10$ notes of $Rs.50$ and $15$ notes of $Rs.100$.