The cost of Compressed Natural Gas (CNG) per litre is increased by 65%. By what percentage must Manish reduce his consumption of CNG so as not to increase his expenditure? (correct up to two decimal places)

The correct option is 39.39%.

Let us understand the relationship between price, consumption, and expenditure step-by-step.
The total expenditure on Compressed Natural Gas (CNG) is given by the formula:
Expenditure = Price per litre × Consumption (in litres)

Let the initial price of CNG per litre be $P$ and the initial consumption of CNG be $C$.
Therefore, the initial expenditure is:
$E_{\text{initial}}=P\times C$

According to the problem, the cost of CNG per litre is increased by 65%.
The new price per litre ($P_{\text{new}}$) becomes:
$P_{\text{new}}=P+0.65P=1.65P$

Let the new consumption be $C_{\text{new}}$.
Since Manish wants to keep his expenditure unchanged, the new expenditure must equal the initial expenditure:
$E_{\text{new}}=E_{\text{initial}}$
$1.65P\times C_{\text{new}}=P\times C$

Dividing both sides by $P$ (assuming price is non-zero):
$1.65\times C_{\text{new}}=C$
$C_{\text{new}}=\frac{C}{1.65}=\frac{C}{165/100}=\frac{100}{165}C=\frac{20}{33}C$

Now, let us calculate the reduction in consumption:
Reduction in Consumption = $C-C_{\text{new}}$
$\text{Reduction}=C-\frac{20}{33}C=\frac{13}{33}C$

The percentage reduction in consumption is:
Percentage Reduction = $\left(\frac{\text{Reduction}}{\text{Initial Consumption}}\right)\times 100$
$\text{Percentage Reduction}=\left(\frac{\frac{13}{33}C}{C}\right)\times 100=\frac{1300}{33}\%$

Performing the division:
$1300÷33\approx 39.3939\%$

Rounding to two decimal places, we get:
Percentage Reduction ≈ 39.39%