Understanding the Petrol Price Hike Problem

This problem asks us to figure out how much a person needs to reduce their monthly travel distance to keep their total petrol expenditure the same, after the price of petrol has increased. We are given the original price, the percentage increase, the monthly travel distance, and the car's mileage.

Step-by-Step Solution Calculation

Calculate New Petrol Price

The original price of petrol was ₹90 per litre. It shot up by 10%. To find the new price, we add the increase amount to the original price.

Increase amount = 10% of ₹90

Increase amount = \( \frac{10}{100} \times 90 = \frac{1}{10} \times 90 = 9 \)

The increase in price is ₹9 per litre.

New Petrol Price = Original Price + Increase amount

New Petrol Price = ₹90 + ₹9 = ₹99 per litre.

Calculate Monthly Fuel Consumption Before Hike

The person travels 2200 km every month, and the car gives a mileage of 16 km per litre. To find out how many litres of petrol are consumed per month, we divide the total distance by the mileage.

Monthly Fuel Consumption = Total Distance / Mileage

Monthly Fuel Consumption = \( \frac{2200 \text{ km}}{16 \text{ km/litre}} \)

Let's perform the division:

• \( \frac{2200}{16} = \frac{1100}{8} = \frac{550}{4} = \frac{275}{2} = 137.5 \)

So, the monthly fuel consumption is 137.5 litres.

Calculate Original Monthly Expenditure

Before the hike, the price was ₹90 per litre, and the person consumed 137.5 litres. The original monthly expenditure is the consumption multiplied by the original price.

Original Monthly Expenditure = Monthly Fuel Consumption \( \times \) Original Price

Original Monthly Expenditure = \( 137.5 \text{ litres} \times \text{₹}90/\text{litre} \)

Original Monthly Expenditure = \( 137.5 \times 90 \)

\( 137.5 \times 90 = (137 + 0.5) \times 90 = 137 \times 90 + 0.5 \times 90 \)

\( 137 \times 90 = 137 \times 9 \times 10 = (1233) \times 10 = 12330 \)

\( 0.5 \times 90 = \frac{1}{2} \times 90 = 45 \)

Original Monthly Expenditure = \( 12330 + 45 = 12375 \)

The original monthly expenditure on petrol was ₹12375.

Determine Maximum Fuel for Original Expenditure After Hike

The person wants to maintain the expenditure at the previous level, which is ₹12375. After the hike, the new petrol price is ₹99 per litre. To find out how many litres can be bought with ₹12375 at the new price, we divide the desired expenditure by the new price.

Maximum Fuel Consumption (at new price) = Original Monthly Expenditure / New Petrol Price

Maximum Fuel Consumption = \( \frac{₹12375}{₹99/\text{litre}} \)

\( \frac{12375}{99} \)

Both 12375 and 99 are divisible by 9 (sum of digits of 12375 is 18, sum of digits of 99 is 18).

\( 99 \div 9 = 11 \)

\( 12375 \div 9 = 1375 \)

So we have \( \frac{1375}{11} \).

Let's divide 1375 by 11:

• \( 11 \times 100 = 1100 \). \( 1375 - 1100 = 275 \).
• \( 11 \times 20 = 220 \). \( 275 - 220 = 55 \).
• \( 11 \times 5 = 55 \). \( 55 - 55 = 0 \).
• So, \( 1375 = 11 \times 100 + 11 \times 20 + 11 \times 5 = 11 \times (100 + 20 + 5) = 11 \times 125 \).

Maximum Fuel Consumption = 125 litres.

Calculate Maximum Travel Distance Possible After Hike

With the new price, the person can afford 125 litres of petrol while maintaining the original expenditure. The car's mileage is still 16 km per litre. The maximum distance that can be travelled is the maximum fuel consumption multiplied by the mileage.

Maximum Travel Distance = Maximum Fuel Consumption \( \times \) Mileage

Maximum Travel Distance = \( 125 \text{ litres} \times 16 \text{ km/litre} \)

\( 125 \times 16 = 125 \times (10 + 6) = 125 \times 10 + 125 \times 6 \)

\( 125 \times 10 = 1250 \)

\( 125 \times 6 = 750 \)

Maximum Travel Distance = \( 1250 + 750 = 2000 \) km.

After the petrol price hike, the person can only travel 2000 km to maintain their original expenditure.

Calculate Required Reduction in Travel Distance

The original monthly travel distance was 2200 km. To maintain the expenditure, the new maximum travel distance is 2000 km. The reduction in travel distance is the difference between the original distance and the new maximum distance.

Reduction in Travel Distance = Original Monthly Distance - Maximum Travel Distance

Reduction in Travel Distance = \( 2200 \text{ km} - 2000 \text{ km} \)

Reduction in Travel Distance = 200 km.

The person should reduce his travel by 200 km every month to maintain his expenditure at the previous level.

Revision Table: Petrol Expenditure Calculation

Additional Information: Managing Expenditure with Price Changes

This problem demonstrates a common real-life scenario where rising costs impact household budgets. When the price of a commodity like petrol increases, individuals or families have a few options to manage their expenditure:

• Reduce Consumption: As shown in this problem, reducing the amount consumed (by travelling less) is one way to keep the total spending constant.
• Increase Expenditure: If the consumption remains the same, the total expenditure will increase according to the new price.
• Find Alternatives: Switch to a more fuel-efficient vehicle, use public transport, carpool, or cycle/walk for shorter distances.
• Increase Income: Find ways to earn more money to cover the increased cost without changing consumption habits.

Understanding concepts like percentage increase, calculating costs based on quantity and price, and working with mileage helps in managing personal finances effectively in the face of price fluctuations.