Question

If the price of cooking gas increases by $36\%$ then by what percent should a family decrease the consumption of cooking gas. So that their expenditure on cooking gas remains the same as earlier?

Answer 1

Step 1. Find the price of cooking gas after increase in price:

Let the original price of cooking gas be $x$

New price of cooking gas $=x+36\%$

$$\begin{gathered} \Rightarrow x+\frac{36}{100} \\ \Rightarrow \frac{136x}{100} \end{gathered}$$

Step 2. Find the decrease on consumption

Let $y$ be the percentage to be reduced from the consumption of

Now, for the expenditure to be the same as earlier is $\frac{136x}{100}\left(1-y\%\right)=x$

$$\begin{gathered} \therefore \frac{136x}{100}\left(1-y\%\right)=x \\ \Rightarrow \frac{136}{100}\left(1-\frac{y}{100}\right)=1 \\ \Rightarrow 1-\frac{y}{100}=\frac{100}{136} \\ \Rightarrow 1-\frac{100}{136}=\frac{y}{100} \\ \Rightarrow \frac{36}{136}=\frac{y}{100} \\ \Rightarrow y=\frac{3600}{136} \\ \Rightarrow y=26\% \end{gathered}$$

Hence, the decrease in consumption of the family is $26\%$.