A bag contains Rs. 180. In which Rs. 1, 50p, 25p coins. Their ratio are 2 : 3:4. Then find number of all types of coins separately.

Options

A. `40,60,80`
B. `160,120,180`
C. `80,120,160`
D. `80,120,150`

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the ratio of coins
The ratio of the coins is given as Rs. 1 : 50p : 25p = 2 : 3 : 4. This means:
- Let the number of Rs. 1 coins be \( 2k \)
- Let the number of 50p coins be \( 3k \)
- Let the number of 25p coins be \( 4k \)

### Step 2: Calculate the total value of each type of coin
Next, we need to calculate the total value contributed by each type of coin:
- The value of Rs. 1 coins = \( 2k \times 1 = 2k \) rupees
- The value of 50p coins = \( 3k \times 0.5 = \frac{3k}{2} \) rupees
- The value of 25p coins = \( 4k \times 0.25 = k \) rupees

### Step 3: Set up the equation for the total amount
The total amount in the bag is Rs. 180. Therefore, we can write the equation:
\[ 2k + \frac{3k}{2} + k = 180 \]

### Step 4: Combine like terms
To combine the terms, we need a common denominator. The common denominator for the terms is 2:
\[ 2k + \frac{3k}{2} + k = 180 \]
Converting \( k \) to have a denominator of 2:
\[ 2k + \frac{3k}{2} + \frac{2k}{2} = 180 \]
This simplifies to:
\[ \frac{4k + 3k + 2k}{2} = 180 \]
\[ \frac{9k}{2} = 180 \]

### Step 5: Solve for \( k \)
Now, we can solve for \( k \):
\[ 9k = 180 \times 2 \]
\[ 9k = 360 \]
\[ k = \frac{360}{9} = 40 \]

### Step 6: Find the number of each type of coin
Now that we have \( k \), we can find the number of each type of coin:
- Number of Rs. 1 coins = \( 2k = 2 \times 40 = 80 \)
- Number of 50p coins = \( 3k = 3 \times 40 = 120 \)
- Number of 25p coins = \( 4k = 4 \times 40 = 160 \)

### Final Answer
Thus, the number of each type of coin is:
- Rs. 1 coins: 80
- 50p coins: 120
- 25p coins: 160

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