The price of petrol increases by 20% and therefore a motor rider decreases his consumption by 10%, by what percent expenditure changes

Question: The price of petrol increases by 20% and therefore a motor rider decreases his consumption by 10%, by what percent expenditure changes ?

• 5 %
• 6 %
• 7 %
• 8 %

Answer: 

• $A$ = percentage increase in price (+20%)
• $B$ = percentage decrease in consumption (-10%)

📌📌Using AB METHOD:-

$$\text{Net change} = 20 + (-10) + \frac{(20 \times -10)}{100}$$ $$= 20 - 10 - 2$$ $$= 8\%$$

'_'  the expenditure increases by 8%.

✅✅ Detail Solution:

Let the initial price of petrol be ₹100 per liter, and let the initial consumption be 100 liters.

Initial Expenditure:

$$\text{Initial expenditure} = \text{Price per liter} \times \text{Quantity consumed}$$ $$= 100 \times 100 = ₹10,000$$

New Price  & New Consumption:

• The price increases by 20%, so the new price per liter: $$100 + (20\% \text{ of } 100) = 100 + 20 = ₹120$$
• The consumption decreases by 10%, so the new quantity: $$100 - (10\% \text{ of } 100) = 100 - 10 = 90 \text{ liters}$$

New Expenditure:

$$\text{New expenditure} = 120 \times 90 = ₹10,800$$

📌📌Percentage Change in Expenditure:

$$\frac{\text{New expenditure} - \text{Initial expenditure}}{\text{Initial expenditure}} \times 100$$ $$= \frac{10,800 - 10,000}{10,000} \times 100$$ $$= \frac{800}{10,000} \times 100$$ $$= 8\%$$

"_"  the expenditure increases by 8%.

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