Question

The price of petrol goes up by 10 percent. By how much percent must a motorists reduce the consumption of petrol so that the expenditure on it remain unchanged?​

Answer 1

Answer:

9.09%

Step-by-step explanation:

Given:

The price of petrol goes up by 10%.

To Find:

By how much percentage the motorist reduce the consumption of petrol so that the expenditure on it remains unchanged?

Procedure:

Let's assume the original price of petrol as 100Rs.

$\sf the \: price \: after \: 10\% \: increase \: = \: \bigg( \dfrac{(100 + 10)}{ \cancel{100}} \bigg) \times \cancel{100}$

$\sf the \: price \: after \: 10\% \: increase \: = \: 100 + 10 = 110$

Reduction to be made so as to make the expenditure unchanged:

$\sf \: Reduction \: to \: be \: made \: so \: as \: to \: make \: the \: expenditure \: unchanged = \dfrac{(110-100)}{110} \times 100$

$\sf \: Reduction \: to \: be \: made \: so \: as \: to \: make \: the \: expenditure \: unchanged = \dfrac{(10 \times 10)}{11}$

$\sf \: Reduction \: to \: be \: made \: so \: as \: to \: make \: the \: expenditure \: unchanged = 9.09\%$

Which means that the motorist needs to reduce the consumption of petrol by 9.09% so as to make the expenditure unchanged.