The price of oil is increased by 20%. However, the expenditure on it increases by 15%. What is the percentage increase or decrease in the consumption of oil?

Options

A. `6^(1/4)%` decrease
B. `4^(1/6)%` decreas
C. `4^(1/6)%` increase
D. `6^(1/4)%` increase

Answer

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

### Step 1: Determine the Initial Consumption and Price
Assume the initial price of oil is \( P = 100 \) per litre and the initial consumption is \( C = 100 \) litres.

### Step 2: Calculate Initial Expenditure
The initial expenditure (E) can be calculated as:
\[ E = P \times C = 100 \times 100 = 10,000 \]

### Step 3: Calculate New Price After 20% Increase
The new price after a 20% increase can be calculated as:
\[ \text{New Price} = P + (20\% \text{ of } P) = 100 + (0.20 \times 100) = 100 + 20 = 120 \]

### Step 4: Calculate New Expenditure After 15% Increase
The new expenditure after a 15% increase can be calculated as:
\[ \text{New Expenditure} = E + (15\% \text{ of } E) = 10,000 + (0.15 \times 10,000) = 10,000 + 1,500 = 11,500 \]

### Step 5: Calculate New Consumption
Now, we can find the new consumption (C') using the new price and new expenditure:
\[ C' = \frac{\text{New Expenditure}}{\text{New Price}} = \frac{11,500}{120} \]
Calculating this gives:
\[ C' = \frac{11,500}{120} = 95.8333 \text{ litres (approximately)} \]

### Step 6: Calculate the Change in Consumption
The change in consumption can be calculated as:
\[ \text{Change in Consumption} = C' - C = 95.8333 - 100 = -4.1667 \text{ litres} \]

### Step 7: Calculate the Percentage Change in Consumption
To find the percentage change in consumption, we use the formula:
\[ \text{Percentage Change} = \left(\frac{\text{Change in Consumption}}{\text{Initial Consumption}}\right) \times 100 \]
Substituting the values gives:
\[ \text{Percentage Change} = \left(\frac{-4.1667}{100}\right) \times 100 = -4.1667\% \]

### Final Answer
Thus, the percentage decrease in the consumption of oil is approximately:
\[ \text{Percentage Decrease} = 4 \frac{1}{6}\% \]

---