A bag contains one rupees, fifty paisa and 25 paisa in the ratio of 8:9:11, if the total amount in the bag is 122, find no. Of coins of each type?

Sure, let's solve this step by step:

1. First, let's understand the ratio given. The ratio of one rupee, fifty paisa, and twenty-five paisa coins is 8:9:11. This means for every 8 one rupee coins, there are 9 fifty paisa coins and 11 twenty-five paisa coins.

2. The total amount in the bag is 122 rupees. We need to convert all the amounts to the same unit to solve this problem. So, let's convert everything to paisa. 1 rupee = 100 paisa. So, 122 rupees = 12200 paisa.

3. Now, let's assign the ratios to the amounts. Let's say 8x is the amount in one rupee coins, 9x is the amount in fifty paisa coins, and 11x is the amount in twenty-five paisa coins.

4. Since we know the total amount, we can form the equation: 100(8x) + 50(9x) + 25(11x) = 12200.

5. Simplifying this equation gives: 800x + 450x + 275x = 12200.

6. Adding all the terms on the left side gives: 1525x = 12200.

7. Solving for x gives: x = 12200 / 1525 = 8.

8. Now, we can find the number of each type of coin by substitifying x = 8 into the ratios:

   • The number of one rupee coins is 8x = 8*8 = 64.
   • The number of fifty paisa coins is 9x = 9*8 = 72.
   • The number of twenty-five paisa coins is 11x = 11*8 = 88.

So, there are 64 one rupee coins, 72 fifty paisa coins, and 88 twenty-five paisa coins.