In how many ways can a person pay an amount ₹120 using two-rupee or five-rupee coins?

To solve this problem, we need to find the number of solutions to the equation 2x + 5y = 120 where x and y are non-negative integers.

Step 1: Start with the maximum number of two-rupee coins that can be used to make ₹120. This is 120/2 = 60. So, the maximum value of x is 60.

Step 2: Start decreasing the value of x (number of two-rupee coins) and for each value of x, find a value of y (number of five-rupee coins) that satisfies the equation.

Step 3: For each value of x, if a corresponding value of y can be found such that y is a non-negative integer, then that is a valid solution.

Step 4: Continue this process until you reach a value of x for which y becomes negative.

Step 5: Count the number of valid solutions. This will give you the number of ways in which a person can pay an amount of ₹120 using two-rupee or five-rupee coins.

Note: This problem assumes that there is an unlimited supply of both two-rupee and five-rupee coins.