If the price of petrol is increased by `20%`. By how much liter of consumption is decreased. So that the expenditure of month will be constant. When his original use is `36` litre.

Options

A. `5`
B. `6`
C. `7`
D. `8`

Answer

To solve the problem step by step, we need to determine how much the consumption of petrol decreases when the price increases by 20%, while keeping the monthly expenditure constant.

### Step 1: Understand the Price Increase
The price of petrol has increased by 20%. This means if the original price is \( P \), the new price will be:
\[ \text{New Price} = P + 0.2P = 1.2P \]

### Step 2: Calculate the Original Expenditure
The original consumption of petrol is 36 liters. Therefore, the original expenditure can be calculated as:
\[ \text{Original Expenditure} = \text{Original Price} \times \text{Original Consumption} = P \times 36 \]

### Step 3: Set Up the Equation for Constant Expenditure
To keep the expenditure constant after the price increase, the new expenditure must equal the original expenditure. The new expenditure can be expressed as:
\[ \text{New Expenditure} = \text{New Price} \times \text{New Consumption} \]
Let \( C \) be the new consumption. Then:
\[ 1.2P \times C = P \times 36 \]

### Step 4: Simplify the Equation
We can simplify the equation by dividing both sides by \( P \) (assuming \( P \neq 0 \)):
\[ 1.2C = 36 \]

### Step 5: Solve for New Consumption
Now, we can solve for \( C \):
\[ C = \frac{36}{1.2} = 30 \text{ liters} \]

### Step 6: Calculate the Decrease in Consumption
To find out how much the consumption has decreased, we subtract the new consumption from the original consumption:
\[ \text{Decrease in Consumption} = \text{Original Consumption} - \text{New Consumption} = 36 - 30 = 6 \text{ liters} \]

### Final Answer
The decrease in consumption is **6 liters**.

---