We need to find how many ways we can make Rs. 107 using Rs. 1, Rs. 10, and Rs. 50 coins.

Equation:

$x + 10y + 50z = 107$ Where: $x$ is the number of Rs. 1 coins $y$ is the number of Rs. 10 coins $z$ is the number of Rs. 50 coins

Case 1:

$z = 0$ Equation: $x + 10y = 107$ Possible values of $y$: 0 to 10 (11 solutions)

Case 2:

$z = 1$ Equation: $x + 10y = 57$ Possible values of $y$: 0 to 5 (6 solutions)

Case 3:

$z = 2$ Equation: $x + 10y = 7$ Possible values of $y$: 0 to 1 (1 solution)

Total Solutions: 11 (from $z = 0$) + 6 (from $z = 1$) + 1 (from $z = 2$) = 18 solutions