The price (per litre) of petrol increases by 50%. By what percent should its consumption be reduced such that the expenditure on it increases by 23% only?

Correct option is A

The price (per litre) of petrol increases by 50%. By what percent should its consumption be reduced such that the expenditure on it increases by 23% only?

Given:
The price (per litre) of petrol increases by 50%. The expenditure on it increases by 23% 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 + 50% of ₹1 = ₹1 + ₹0.50 = ₹1.5
New expenditure = ₹100 + 23% of ₹100 = ₹100 + ₹23 = ₹123
New expenditure = New price × Reduced consumption
=> ₹123 = ₹1.5 × x
​$$x =\frac{ 123 }{ 1.5} = 82$$
=> x = 82%
Therefore, the consumption should be reduced by 100 - 82 = 18%.

Alternative Method: 

Expenditure = Price $$\times$$ Consumption 

​$$50 \% = \frac{1}{2}$$

Old price = 2 unit , New price = 3 Unit 

Increase Expenditure = 23% 

Old expenditure = 100 unit 

New expenditure = 100 + 23 = 123 unit 

According to formula 

Old Consumption  = $$\frac{100}{2}= 50 \text {unit}$$

New Consumption = $$\frac{123}{3}= 41 \text {unit}$$

Change in expenditure = $$\frac{(50 - 41)}{50}\times 100 \% = 18\%$$

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