If the price of petrol increases by 20%, if there is no increase in the cost of petrol, then the consumption of the supply has to be reduced and the original consumption - what is the ratio of these two?

To solve this, we are dealing with the concept of **elasticity of demand**. Since the price of petrol increases by 20%, we assume no increase in the total cost of consumption, meaning the expenditure remains constant. To maintain this, the consumption must decrease in proportion to the price increase. We want to find the ratio of the new consumption to the original consumption.

### Step-by-step process:

1. Let the original price of petrol be \( P \), and the original consumption be \( Q \). The original expenditure is:
   \[
   \text{Original expenditure} = P \times Q
   \]

2. If the price increases by 20%, the new price becomes:
   \[
   \text{New price} = 1.2 \times P
   \]

3. Let the new consumption be \( Q' \). The new expenditure (which remains the same as the original expenditure) is:
   \[
   \text{New expenditure} = 1.2 \times P \times Q'
   \]

4. Since the expenditure is unchanged, we set the original expenditure equal to the new expenditure:
   \[
   P \times Q = 1.2 \times P \times Q'
   \]

5. Simplifying the equation:
   \[
   Q = 1.2 \times Q'
   \]

6. Solving for \( Q' \):
   \[
   Q' = \frac{Q}{1.2}
   \]

### Ratio of new consumption to original consumption:
The ratio of the new consumption to the original consumption is:
\[
\frac{Q'}{Q} = \frac{1}{1.2} = \frac{5}{6}
\]

Thus, the consumption must decrease to \( \frac{5}{6} \) of the original consumption. 

### Conclusion:
The ratio of new consumption to original consumption is \( \frac{5}{6} \). Therefore, the reduction in consumption is necessary to maintain the same expenditure after a 20% increase in the price of petrol.

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How does this problem relate to the concept of elasticity in economics?
2. What would happen to consumption if the price increase were 50% instead of 20%?
3. How would the ratio change if the price increased by 10%?
4. Can this same approach be used for other goods or commodities with price increases?
5. What assumptions are we making about the consumer's behavior in this problem?

**Tip:** When dealing with proportional changes in price and quantity, setting up a clear equation based on total expenditure can simplify finding the relationship between the variables.

Understand how to calculate the ratio of new consumption to original consumption after a 20% increase in petrol prices. This solution uses the concept of elasticity of demand, showing the mathematical steps and formulas involved. Suitable for students in Grades 9-12.

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