The price (per litre) of petrol increases by 90%. By what percent should its consumption be reduced such that the expenditure on it increases by 33% only?

Correct option is A

Given:

Price of petrol increases by 90%

Total expenditure increases by only 33%

Required: Percentage reduction in consumption

Formula Used:

Expenditure = Price × Consumption

Solution:

Let initial values:

Price = 100

Consumption = 100

Expenditure = 100 × 100 = 10,000

Then after price increase:

New Price = 100 + 90% of 100 = 190

New Expenditure = 10,000 + 33% of 10,000 = 13,300

New Consumption = $$\frac{13,300}{190}$$​= 70

Percentage Reduction = $$\left( \frac{100 - 70}{100} \right) \times 100$$​ = 30%

Alternate Solution:

Price ratio = 100 : 190 = 10 : 19 

Expenditure ratio = 100 : 133 

Consumption Ratio = $$\frac{133}{190}$$​​

So, Initial : Final Consumption = 190 : 133

Reduction = 190 - 133 = 57

Percentage Reduction = $$\left( \frac{57}{190} \right) \times 100$$ = 30%