The price (per litre) of petrol increases by 40%. By what percent should its consumption be reduced such that the expenditure on it increases by 19% only?

Correct option is A

Given:
The price (per litre) of petrol increases by 40%. The expenditure on it increases by 19% only.
Formula used:
New expenditure = Original expenditure × (1 + Increase in expenditure)
Let the original consumption be 100 litres.
Let the reduced consumption be x litres.
New expenditure = New price × Reduced consumption
Solution:
Let the original price be ₹1 per litre (for simplicity).
Original expenditure = 100 × ₹1 = ₹100
New price = ₹1 + 40% of ₹1 = ₹1 + ₹0.40 = ₹1.4
New expenditure = ₹100 + 19% of ₹100 = ₹100 + ₹19 = ₹119
New expenditure = New price × Reduced consumption
=> ₹119 = ₹1.4 × x
​$$x =\frac{ 119 }{ 1.4} = 85$$
=> x = 85%
Therefore, the consumption should be reduced by 100 - 85 = 15%.

Alternative Method: 

Expenditure = Price $$\times$$ Consumption 

​$$40 \% = \frac{2}{5}$$

Old price = 5 unit , New price = 7 Unit 

Increase Expenditure = 19% 

Old expenditure = 100 unit 

New expenditure = 100 + 19 = 119 unit 

According to formula 

Old Consumption  = $$\frac{100}{5}= 20 \text {unit}$$ 

New Consumption = $$\frac{119}{7}= 17 \text {unit}$$  

Change in expenditure = $$\frac{(20 - 17)}{20}\times 100 \% = 15\%$$ 

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