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Fill in the blank:

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

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Detailed Solution

The correct answer is: 9%.
Let the initial price of petrol be x.
Then increase in price is:

I = 10 % x ⇒ I = 10100 × x ⇒ I = 0.1 x

The final price:

F p = x + 0.1 x ⇒ F p = x (1 + 0.1) ⇒ F p = 1.1 x

Let the initial and final consumption be y and z.
Initial expenditure=

x × y

Final expenditure=

F p × z

If initial and final expenditures are equal then there will be no loss

x × y = F p × z ⇒ x × y = 1.1 x × z ⇒ z = y 1.1

So, the final consumption

= 1 1.1

Required %=

1 − 1 1.1 × 100 ≈ 9 %

Consumption should decrease by 9%

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