The expenses on rice. fsb and oll of a family are in the ratio 12:17:3. The prices of these articles are increased by 20%.30% and 50% respectively. The total expenses of family on these articles are increased by

Options

A. 14 `1/8` %
B. 7 `1/8` %
C. 56 `1/8` %
D. 28 `1/8` %

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the Ratios
The expenses on rice, FSB, and oil are given in the ratio of 12:17:3.

### Step 2: Assign Values Based on the Ratio
Let's assign a common multiplier to these ratios. We can let:
- Rice = 12x
- FSB = 17x
- Oil = 3x

### Step 3: Calculate Total Expenses
Now, we can calculate the total expenses:
\[ \text{Total Expenses} = 12x + 17x + 3x = 32x \]

### Step 4: Determine Price Increases
Next, we need to calculate the increase in expenses due to the price increases:
- Rice increases by 20%:
\[ \text{Increase in Rice} = 12x \times 0.20 = 2.4x \]
- FSB increases by 30%:
\[ \text{Increase in FSB} = 17x \times 0.30 = 5.1x \]
- Oil increases by 50%:
\[ \text{Increase in Oil} = 3x \times 0.50 = 1.5x \]

### Step 5: Calculate Total Increase in Expenses
Now, we can find the total increase in expenses:
\[ \text{Total Increase} = 2.4x + 5.1x + 1.5x = 9x \]

### Step 6: Calculate the Percentage Increase
To find the percentage increase, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Total Increase}}{\text{Original Total Expenses}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Increase} = \left( \frac{9x}{32x} \right) \times 100 = \frac{9}{32} \times 100 \]
Calculating this gives:
\[ \text{Percentage Increase} = 28.125\% \]

### Final Answer
The total expenses of the family on these articles are increased by **28.125%**.

---