The prime cost of an article is three times the value of the raw material used. The cost of raw materials increasef in the ratio of 5 : 12 and manufacturing expenses in the ratio 4 : 5 . The article, which originally cost Rs 6, will now cost.

Answer

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

### Step 1: Understand the Prime Cost
The prime cost of an article is defined as the sum of the cost of raw materials and manufacturing expenses. According to the problem, the prime cost is three times the value of the raw materials used.

Let:
- \( R \) = original cost of raw materials
- \( M \) = original manufacturing expenses

From the problem, we have:
\[ \text{Prime Cost} = 3R \]

### Step 2: Determine the Original Cost
The original cost of the article is given as Rs 6. Therefore:
\[ 3R = 6 \]

### Step 3: Calculate the Original Cost of Raw Materials
To find the original cost of raw materials \( R \):
\[ R = \frac{6}{3} = 2 \]

### Step 4: Calculate the Original Manufacturing Expenses
Now, we can find the original manufacturing expenses \( M \) using the prime cost equation:
\[ \text{Prime Cost} = R + M \]
\[ 6 = 2 + M \]
Thus,
\[ M = 6 - 2 = 4 \]

### Step 5: Calculate the New Cost of Raw Materials
The cost of raw materials increased in the ratio of 5:12. Therefore, the new cost of raw materials \( R' \) can be calculated as follows:
\[ R' = R \times \frac{12}{5} \]
\[ R' = 2 \times \frac{12}{5} = \frac{24}{5} = 4.8 \]

### Step 6: Calculate the New Manufacturing Expenses
The manufacturing expenses increased in the ratio of 4:5. Thus, the new manufacturing expenses \( M' \) can be calculated as:
\[ M' = M \times \frac{5}{4} \]
\[ M' = 4 \times \frac{5}{4} = 5 \]

### Step 7: Calculate the New Prime Cost
Now, we can find the new prime cost of the article:
\[ \text{New Prime Cost} = R' + M' \]
\[ \text{New Prime Cost} = 4.8 + 5 = 9.8 \]

### Conclusion
The article, which originally cost Rs 6, will now cost Rs 9.8.

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