If the price of petrol is increased by 20%,by what percentage should the consumption be decreased by the consumer, if the expenditure on petrol remains unchanged?

Options

A. `16(2)/(3)%`
B. `6(2)/(3)%`
C. `8%`
D. `15%`

Answer

To solve the problem step by step, we need to determine the percentage decrease in consumption when the price of petrol increases by 20%, while keeping the expenditure constant.

### Step-by-Step Solution:

1. **Understand the relationship between price, consumption, and expenditure**:
- Let the original price of petrol be \( P \).
- Let the original consumption be \( C \).
- The original expenditure on petrol is given by the formula:
\[ \text{Expenditure} = \text{Price} \times \text{Consumption} = P \times C \]

2. **Calculate the new price after the increase**:
- The price of petrol is increased by 20%. Therefore, the new price \( P' \) can be calculated as:
\[ P' = P + 0.20P = 1.20P \]

3. **Set up the equation for unchanged expenditure**:
- Since the expenditure remains unchanged, we can set up the equation:
\[ P \times C = P' \times C' \]
- Substituting \( P' \) into the equation gives:
\[ P \times C = 1.20P \times C' \]

4. **Simplify the equation**:
- Dividing both sides by \( P \) (assuming \( P \neq 0 \)):
\[ C = 1.20 \times C' \]
- Rearranging gives:
\[ C' = \frac{C}{1.20} \]

5. **Calculate the new consumption in terms of percentage**:
- To find the percentage decrease in consumption, we first find the decrease in consumption:
\[ \text{Decrease in consumption} = C - C' = C - \frac{C}{1.20} = C \left(1 - \frac{1}{1.20}\right) \]
- This simplifies to:
\[ C \left(1 - \frac{1}{1.20}\right) = C \left(\frac{1.20 - 1}{1.20}\right) = C \left(\frac{0.20}{1.20}\right) = C \left(\frac{1}{6}\right) \]

6. **Express the decrease as a percentage of the original consumption**:
- The percentage decrease in consumption is then given by:
\[ \text{Percentage decrease} = \left(\frac{\text{Decrease in consumption}}{C}\right) \times 100 = \left(\frac{C \left(\frac{1}{6}\right)}{C}\right) \times 100 = \frac{1}{6} \times 100 \]
- Calculating this gives:
\[ \frac{100}{6} = 16.67\% \]
- Thus, the percentage decrease in consumption is \( 16 \frac{2}{3}\% \).

### Final Answer:
The consumer should decrease their consumption by \( 16 \frac{2}{3}\% \).

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