Solving with a System of Linear Equations

This problem can be solved by setting up two linear equations with two variables based on the information provided about the total number of notes and their total value.

1. Define the Variables

• Let x be the number of Rs. 20 notes.
• Let y be the number of Rs. 50 notes.

2. Formulate the Equations

We can create two equations from the given statements:

1. Equation based on the total number of notes:
   x + y = 324
2. Equation based on the total value of the notes:
   20x + 50y = 12450

3. Solve the System of Equations

We can use the substitution method to solve for x.

From the first equation, we can express y in terms of x:

y = 324 - x

Now, substitute this expression for y into the second equation:

20x + 50(324 - x) = 12450

Distribute the 50:

20x + 16200 - 50x = 12450

Combine the terms with x:

-30x + 16200 = 12450

Rearrange the equation to solve for x:

16200 - 12450 = 30x

3750 = 30x

x = 3750 / 30

x = 125

Conclusion

The number of Rs. 20 notes is 125.