Question

the price of petrol goes up by 10% by how much percent must a motorist reduce the consumption of petrol so that the expenditure on it remains unchanged?​

Answer 1

Answer:

9.09 %

Step-by-step explanation:

Let the initial price of petrol be Rs. x

Then, price after increase of 10 % = 100 + (100*10)/100

= 100 + 10 

Price after increase of 10 % = Rs. 110

Now,

Reduction in consumption of petrol in percent = [{(110 - 100)}*100]/110

⇒ (10*100)/110

⇒ 100/11

⇒ 9.09 %

So, the motorists have to reduce the consumption of petrol by 9.09 %, so that the expenditure on it remains unchanged.

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Answer 2

$\large\underline\pink{Given:-}$

• The price of petrol goes up by 10%.

$\large\underline\pink{To find:-}$

• how much percent must a motorist reduce the consumption of petrol so that the expenditure on it remains unchanged .....?

$\large\underline\pink{Solutions:-}$

Let the consumption of petrol originally be 1 unit and let it's cost of petrol = 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

$= \: \: {(\frac{1}{100} \: \times \: {100})}$

$= \: \: \frac{10}{11}$

Now, reduction in consumption

$= \: \: {({1} \: - \: \frac{10}{11})}$

$= \: \: {(\frac{{11} \: - \: {10})}{11})}$

$= \frac{1}{11} \: unit.$

Percentage of reduction

$= \: \: {(\frac{1}{11} \: \times \: \frac{1}{1} \: \times \: {100} \%)}$

$= \: \: \frac{100}{11}$

$= \: \: {9.09 \%}$

Hence, A motorist must reduce the consumption of petrol by 9.09%.