Question

If the price of petrol is increased by 20%, by what percentage the consumption should be decreased by the consumer, if the expenditure on petrol remains unchanged?
a. $ 16\dfrac{2}{3}% $
b. $ 6\dfrac{2}{3}% $
c. $ 8% $
d. $ 15% $

Answer 1

Hint: Here, in this question, we can take the original consumption of petrol by the consumer to be 1 liter and its price to be 100 rupees. Then we can find the price of 1 liter of petrol when it is increased by 20%. Using this we can calculate the decreased amount of petrol for the same price and then the percentage decreased which will be our required answer.

Complete step-by-step answer:
In this question, we are asked to find the percentage of the consumption of petrol that should be decreased by the consumer if the price is increased by 20% and the expenditure has to be unchanged.
Let the consumption of petrol by the consumer be 1 liter and the price be 100 rupees per liter.
So, the expenditure is 100 rupees.
When increased by 20%, the price per liter becomes 120 rupees.
Let the new amount of petrol be x liters.
Now, 1 liter costs 120 rupees.
So, x liters cost $ 120x $ .
But the expenditure remains constant.
So, we get,
\[\begin{align}
& 120x=100 \\
& \Rightarrow x=\dfrac{100}{120} \\
& \Rightarrow x=0.83 \\
\end{align}\]120x=100
So, the new amount is \[0.83\dfrac{1}{3}\]liters.
The amount decreased is \[1-0.83\dfrac{1}{3}=0.16\dfrac{2}{3}\] liters.
So, the decreased percentage is $ \dfrac{0.16\dfrac{2}{3}}{1}\times 100=16\dfrac{2}{3}%.............(1.1) $
Therefore, from equation 1.1, we get the correct option to the given question is option (a)
 $ 16\dfrac{2}{3}% $ .


Note: In this sort of question, we must be careful while calculating the price of one liter and then the amount of the substance as a small mistake in these little things will make us arrive at a wrong answer instead of the correct one. Also, while adding and subtracting improper fractions, the Lowest common multiples of the denominators are to be taken as the denominator of the result and the numerators are to be multiplied as required and then the operation should take place.