Question

In the new budget, the price of petrol rose by $10\%$. By how much percent must one reduce the consumption so that the expenditure does not increase?

Answer 1

We have to reduce the consumption such that the expenditure does not increase.

Let the initial price of the petrol is $x$.

Given that the petrol price is rose by $10\%$ in the new budget, then the increase in petrol price is given by

$I=10\%$ of $x$

$\Rightarrow I=\frac{10}{100}\times x$

$\Rightarrow I=0.1x$

Now the final price of the petrol after new budget is given by

$F_p=x+0.1x$

$\Rightarrow F_p=x(1+0.1)$

$\Rightarrow Fp=1.1x$

Let the initial and final consumption are $y$ and $z$ respectively.

Now the initial expenditures are $x\times y$.

Final expenditures are $Fp\times z$

If the initial expenditures are equal to final expenditures, then only there is no loss.

So, $x\times y=Fp\times z$

$\Rightarrow x\times y=1.1x\times z$

$\Rightarrow z=\frac{y}{1.1}$

So, the final consumption should be equal to $\dfrac{1]{1.1}$ of the initial consumption.

So, the required percentage is $(1-\frac{1}{1.1})\times 100$

$=\frac{0.1}{1.1}\times 100$

$=9.1\%$ (Approximately)

Therefore, The person should decrease his consumption by $9.1\%$ (Approximately)