Question:
The price of petrol goes up by 10%. By how much per cent must a motorist reduce the consumption of petrol so that the expenditure on it remains unchanged?
Solution:
Let the consumption of petrol originally be 1 unit and let its cost be Rs 100 .
New cost of 1 unit of petrol $=$ Rs 110
Now, Rs 110 will yield 1 unit of petrol.
i.e., Rs 100 will yield $\left(\frac{1}{110} \times 100\right)$, i.e., $\frac{10}{11}$ units of petrol.
Now, reduction in consumption $=\left(1-\frac{10}{11}\right)=\frac{1}{11}$ unit
Percentage of reduction $=\left(\frac{1}{11} \times \frac{1}{1} \times 100\right) \%=9 \frac{1}{11} \%$
$\therefore$ A motorist must reduce the consumption of petrol by $9 \frac{1}{11} \%$.