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 14% only?

Correct option is D

Given:

Price of petrol increases by 50%.

Expenditure should increase by only 14%.

Concept Used:

Expenditure = Price × Quantity.

If price increases by x% and we want total expenditure to increase by only y%, then required consumption is adjusted as:

​$$(1 + \frac{x}{100})(1 - \frac{r}{100}) = 1 + \frac{y}{100}$$​​

where r% is the required reduction in consumption.

Solution: 

Now, 

​$$(1 + \frac{50}{100})(1 - \frac{r}{100}) = 1 + \frac{14}{100} \\ \ \\1.5 \times (1 - \frac{r}{100}) = 1.14 \\ \ \\1 - \frac{r}{100} = \frac{1.14}{1.5} \\ \ \\1 - \frac{r}{100} = 0.76 \\ \ \\\frac{r}{100} = 0.24$$​​

r = 24%

Thus, Consumption should be reduced by 24%. 

Alternate Solution: 

Decrease in consumption = $$\frac{150-114}{150}\times 100 = \frac{36}{150}\times 100 = 24\%$$​​