Given Information:
- Bansi has 3 times as many two-rupees coins as he has five-rupee coins.
- Bansi has a total sum of Rs. 77.

Let's assume:
- Let x be the number of five-rupee coins Bansi has.
- Let 3x be the number of two-rupee coins Bansi has.

Value Calculation:
- The value of one five-rupee coin is Rs. 5.
- The value of one two-rupee coin is Rs. 2.

Equation 1:
- The total value of the five-rupee coins = 5x.

Equation 2:
- The total value of the two-rupee coins = 2(3x) = 6x.

Equation 3:
- The total sum of the coins = Rs. 77.

Equation 4:
- The total value of the coins = total value of five-rupee coins + total value of two-rupee coins.
- 77 = 5x + 6x = 11x.

Solution:
- Solving Equation 4, we find x = 7.
- Bansi has 7 five-rupee coins and 3x = 3(7) = 21 two-rupee coins.

Explanation:
- Let's break down the solution step by step to understand it clearly:
- We assume the number of five-rupee coins Bansi has as x.
- According to the given information, Bansi has 3 times as many two-rupee coins as he has five-rupee coins. Therefore, the number of two-rupee coins is 3x.
- To calculate the total value of the five-rupee coins, we multiply the value of one coin (Rs. 5) by the number of five-rupee coins (x). This gives us 5x.
- Similarly, to calculate the total value of the two-rupee coins, we multiply the value of one coin (Rs. 2) by the number of two-rupee coins (3x). This gives us 6x.
- We know that the total sum of the coins is Rs. 77. Therefore, we can set up the equation 5x + 6x = 77.
- Simplifying this equation, we get 11x = 77.
- Solving for x, we find x = 7.
- This means Bansi has 7 five-rupee coins and 3x = 3(7) = 21 two-rupee coins.