In a purse there are 20-rupee notes 10-rupee notes and 5-rupee notes. the number of 5-rupee notes exceeds two times the 10-rupee notes by one. the 20-rupee notes are 5 less than the 10-rupee notes. if the total value of the money in the purse is Rs185 find the number of each variety of notes.

Let #10-rupee = x, then #5-rupee = 2x+1 and #20-rupee = x-5.

x + (2x+1) + (x-5) = 185

Solve for x, then the other expressions.

To find the number of each variety of notes, we can set up a system of equations based on the given information.

Let's denote the number of 20-rupee notes as 'x', the number of 10-rupee notes as 'y', and the number of 5-rupee notes as 'z'.

We are given the following information:

1) The number of 5-rupee notes exceeds two times the 10-rupee notes by one:
z = 2y + 1

2) The 20-rupee notes are 5 less than the 10-rupee notes:
x = y - 5

3) The total value of the money in the purse is Rs185:
20x + 10y + 5z = 185

Now, we can solve this system of equations to find the values of 'x', 'y', and 'z'.

Substituting equation (2) into equation (1), we have:
z = 2(y - 5) + 1
z = 2y - 9

Substituting equations (2) and (3) into equation (3), we have:
20(y - 5) + 10y + 5(2y - 9) = 185
20y - 100 + 10y + 10y - 45 = 185
40y - 145 = 185
40y = 330
y = 8.25

Since the number of notes must be a whole number, we can round y to the nearest whole number. Thus, y = 8.

Substituting the value of y into equation (2), we have:
x = 8 - 5
x = 3

Substituting the values of x and y into equation (1), we have:
z = 2(8) + 1
z = 16 + 1
z = 17

Therefore, there are 3 twenty-rupee notes, 8 ten-rupee notes, and 17 five-rupee notes in the purse.