Question

The price of petrol goes up by $10\%$. By how much percent must a motorist reduce the consumption of petrol so that expenditure on it remains unchanged?

Answer 1

Let the initial price of $1$ litre of petrol be $Rs.100$

Increase in price of petrol (in $\%)=10\%$

Price of petrol after increament $=100+10\%of100$

$=100+\frac{10}{100}\times 100$

$=100+0.10\times 100=100+10=Rs.110$

so, now he will get 1 litre of petrol in $Rs.110.$

$Rs.110\to 1litre$

$Rs.100\left(initialpricewhichhewantstospend\right)\to ?litre\left[supposexlitre\right]$

$\therefore$ By ratio method, $\frac{Rs.110}{1litre}=\frac{Rs.100}{xlitre}$

$\Rightarrow x=\frac{100}{110}litre$

Now, he has to reduce the petrol consumption by $(1-\frac{100}{110}litre)=\frac{10}{110}litre$

Reduction in petrol consumption (in $\%)=\frac{Reducedamount}{original}\times 100$

$=\frac{\frac{10}{110}}{1}\times 100$

$=\frac{10}{11}\times 10$

$=\frac{100}{11}=9.09\%$