Question

The price of LPG increases by \(16\%\). By what percentage should consumption be reduced so that the total expenditure remains the same?

• A. \(13.79\%\)
• B. \(16.67\%\)
• C. \(13.30\%\)
• D. \(15.26\%\)

Hint:

For constant expenditure: \[ \text{Reduction \%}=\frac{\text{Increase \%}}{100+\text{Increase \%}}\times100 \] This shortcut saves a lot of time in competitive exams.

Answer 1

The Correct Option is A

Step 1: Fix easy starting numbers.
Let the old price be $100$ and the old consumption be $1$ unit, so the old expenditure is $100\times 1=100$.
Step 2: Raise the price by 16 percent.
The new price becomes \[ 100+16=116 \]
Step 3: Keep the expenditure unchanged.
We want new price times new consumption to stay $100$, so \[ 116\times c = 100 \]
Step 4: Solve for the new consumption.
\[ c=\frac{100}{116}=0.8620\ldots \]
Step 5: Find how much consumption fell.
The drop is \[ 1-0.8620\ldots = 0.1379\ldots \] of the original.
Step 6: Express the drop as a percentage.
\[ 0.1379\ldots \times 100 = 13.79\% \] So the consumer must cut usage by about $13.79\%$.
\[ \boxed{13.79\%} \]