In a pocket of A, the ratio of Rs. 1 coins, 50p coins and 25p coins can be expressed by three consecutive odd prime numbers that are in ascending order. The total value of coins in the bag is Rs 58. If the number of Rs. 1, 50p, 25p coins are reversed, find the new total value of coins in the pocket of A?

Options

A. Rs 68
B. Rs 43
C. Rs 75
D. Rs 82

Answer

To solve the problem, we need to follow these steps:

### Step 1: Identify the ratio of coins
The ratio of Rs. 1 coins, 50p coins, and 25p coins is expressed by three consecutive odd prime numbers in ascending order. The first three consecutive odd prime numbers are 3, 5, and 7.

### Step 2: Assign variables based on the ratio
Let:
- The number of Rs. 1 coins = 3x
- The number of 50p coins = 5x
- The number of 25p coins = 7x

### Step 3: Calculate the total value of the coins
The total value of the coins can be calculated as follows:
- Value of Rs. 1 coins = 3x * 1 = 3x Rs.
- Value of 50p coins = 5x * 0.5 = 2.5x Rs.
- Value of 25p coins = 7x * 0.25 = 1.75x Rs.

Now, adding these values together:
Total value = 3x + 2.5x + 1.75x = 7.25x Rs.

### Step 4: Set up the equation based on the total value
According to the problem, the total value of coins is Rs. 58. Therefore, we can set up the equation:
7.25x = 58

### Step 5: Solve for x
To find x, we divide both sides of the equation by 7.25:
x = 58 / 7.25
x = 8

### Step 6: Calculate the number of each type of coin
Now, we can find the number of each type of coin:
- Number of Rs. 1 coins = 3x = 3 * 8 = 24
- Number of 50p coins = 5x = 5 * 8 = 40
- Number of 25p coins = 7x = 7 * 8 = 56

### Step 7: Reverse the number of coins
If the number of Rs. 1, 50p, and 25p coins are reversed, we have:
- Number of Rs. 1 coins = 56
- Number of 50p coins = 40
- Number of 25p coins = 24

### Step 8: Calculate the new total value of the coins
Now we calculate the new total value:
- Value of Rs. 1 coins = 56 * 1 = 56 Rs.
- Value of 50p coins = 40 * 0.5 = 20 Rs.
- Value of 25p coins = 24 * 0.25 = 6 Rs.

Adding these values together gives us:
New total value = 56 + 20 + 6 = 82 Rs.

### Final Answer
The new total value of coins in the pocket of A is Rs. 82.

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