If the price of cooking gas increase by 36%by what percentage should a family decrease its consumption of cooking gas so that expenditure on cooking gas remains same as earlier

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Solution

Let x be the Initial price of the gas

Let y be the initial consumption of cooking gas .

Total Expenditure = Price of the gas * Consumption = xy.

Price of cooking gas increase by 36%

So new price of the gas = x + 36x /100 = 1.36x

Let new household consumption be a.

Final Expanditure will be 1.36x * a

In order to not let the expenditure increase

Initial expenditure = final expenditure

xy = 1.36xa

a=100y/136.

So final consumption we got is 100y/136 part

Decrease in consumption = y - 100y/136 = (136y-100y)/136 = 36 y /136

Thus, consumption should decrease by = (36/136)*100% = 26..47%

Answer : 26..47%

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