Three friends A, B and C, share a cake in the ratio 5:7:4. The cake costs 96. How much does each one have to pay for his share ?

Answer

To solve the problem of how much each friend A, B, and C has to pay for their share of the cake, we can follow these steps:

### Step 1: Understand the Ratio
The friends share the cake in the ratio of 5:7:4. This means:
- A's share = 5 parts
- B's share = 7 parts
- C's share = 4 parts

### Step 2: Calculate the Total Parts
To find the total parts shared among A, B, and C, we add the parts of the ratio together:
\[ \text{Total parts} = 5 + 7 + 4 = 16 \]

### Step 3: Determine the Cost per Part
The total cost of the cake is Rs. 96. To find the cost of each part, we divide the total cost by the total number of parts:
\[ \text{Cost per part} = \frac{96}{16} = 6 \]

### Step 4: Calculate Each Friend's Share
Now we can calculate how much each friend has to pay based on their share in the ratio:

- **A's share**:
\[ \text{A's share} = 5 \times \text{Cost per part} = 5 \times 6 = 30 \]

- **B's share**:
\[ \text{B's share} = 7 \times \text{Cost per part} = 7 \times 6 = 42 \]

- **C's share**:
\[ \text{C's share} = 4 \times \text{Cost per part} = 4 \times 6 = 24 \]

### Step 5: Verify the Total Cost
To ensure our calculations are correct, we can add the shares of A, B, and C together:
\[ \text{Total cost} = A's share + B's share + C's share = 30 + 42 + 24 = 96 \]

### Final Answer
- A has to pay Rs. 30
- B has to pay Rs. 42
- C has to pay Rs. 24

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