Question

The price of petrol is increased by 25%. By how much percent should a car owner reduce his consumption of petrol so that the expenditure on petrol would not increase?

Answer 1

Hint: Here, we can use the definition of percentage. First of all, we can assume his consumption to be x and the cost of petrol to be y. Then, we can find the total money spent by him on petrol earlier as well as after the rise of price. Equating both of them will give us the percentage to which he will reduce the consumption.
Complete step-by-step answer:
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, ‘%’. A percentage is a dimensionless number. The percentage value is calculated by multiplying the numeric value of the ratio or fraction by 100.
Let us assume that earlier he consumed ‘x’ amount of petrol in his car.
Also assume that the consumption now is a% of x.
So, we can write:
Amount of petrol consumed now = $\dfrac{a}{100}\times x$
Now, let us take the price of petrol to be y.
So, earlier the total expenses on petrol = $x\times y........\left( 1 \right)$
Since, the price of petrol has increased by 25%. So, new price of petrol will be:
$\text{New price of petrol =}\dfrac{25\times y}{100}+y=y+\dfrac{y}{4}=\dfrac{5y}{4}$
Therefore, after reducing consumption, the total expense on petrol will be:
$=\dfrac{a}{100}\times x\times \dfrac{5y}{4}.........\left( 2 \right)$
So, in order to keep the expenses the same, equation (1) and equation (2) must give the same value. So, on equating (1) and (2), we get:
$\begin{align}
  & x\times y==\dfrac{a}{100}\times x\times \dfrac{5y}{4} \\
 & \Rightarrow x\times y\times 400=5a\times x\times y \\
 & \Rightarrow 5a=400 \\
 & \Rightarrow a=\dfrac{400}{5} \\
 & \Rightarrow a=80 \\
\end{align}$
This means that now he consumes 80% of the petrol he consumed earlier.
So, we can say that he has to reduce his consumption by $\left( 100-80 \right)\%=20\%$.
Hence, the car owner should reduce his consumption of petrol by 20% so that the expenditure on petrol would not increase.
Note: Students should note here that we have taken ‘a’ as the amount of petrol that he consumes now and we subtracted it from the whole in order to get the reduction in consumption of petrol. The calculations must be done properly to avoid unnecessary mistakes.