The price of petrol goes up by 10%.
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 $9 \frac{1}{11} \%$.

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