Problem:
70 coins of value 2 and 5 rupee are mixed in a purse. If the total value is rupees 230. Find the number of coins of each type.

Solution:
Let's assume the number of coins of value 2 rupees as 'x' and the number of coins of value 5 rupees as 'y'.

Equations:
We can create two equations based on the given information:

1. x + y = 70 (Total number of coins)
2. 2x + 5y = 230 (Total value of coins)

Solving the Equations:
We can solve these equations using the elimination method or substitution method to find the values of 'x' and 'y'.

Method 1: Elimination Method

1. Multiply equation 1 by 2:
2(x + y) = 2(70)
2x + 2y = 140

2. Subtract equation 2 from the above equation:
(2x + 2y) - (2x + 5y) = 140 - 230
2x - 2x + 2y - 5y = -90
-3y = -90
Divide both sides by -3:
y = -90 / -3
y = 30

3. Substitute the value of y into equation 1:
x + 30 = 70
x = 70 - 30
x = 40

So, the number of coins of value 2 rupees is 40 and the number of coins of value 5 rupees is 30.

Method 2: Substitution Method

1. Solve equation 1 for x:
x = 70 - y

2. Substitute the value of x into equation 2:
2(70 - y) + 5y = 230
140 - 2y + 5y = 230
Combine like terms:
3y = 230 - 140
3y = 90
Divide both sides by 3:
y = 90 / 3
y = 30

3. Substitute the value of y into equation 1:
x + 30 = 70
x = 70 - 30
x = 40

So, the number of coins of value 2 rupees is 40 and the number of coins of value 5 rupees is 30.

Conclusion:
Therefore, there are 40 coins of value 2 rupees and 30 coins of value 5 rupees in the purse, making a total value of 230 rupees.