There was a hike in petrol price by 12%. By how much percentage should a person decrease his petrol consumption such that there is no change in his expenditure on petrol?

The Correct answer is Option 3.

Key PointsTo determine the percentage decrease in petrol consumption required to maintain the same expenditure after a 12% increase in petrol prices, we can use the following approach:

Let:

• The original price of petrol be  P.
• The original quantity of petrol consumed be  Q.
• The original expenditure on petrol be  E.

⇒ The original expenditure can be expressed as:  E = P × Q 

⇒ After a 12% increase in the price of petrol, the new price becomes: New Price = P + 0.12 P = 1.12 P 

⇒ Let the new quantity of petrol consumed be Q ′ Q ′ . The new expenditure must remain the same as the original expenditure:

⇒ E = New Price × Q ′ = 1.12 P × Q ′

⇒ Setting the original expenditure equal to the new expenditure: P × Q = 1.12 P × Q ′

⇒ We can cancel  P from both sides (assuming P ≠ 0 P =0): Q = 1.12 Now, solving for  ′ Q ′ :

⇒ Q ′ = Q / 1.12  ​

⇒ To find the percentage decrease in consumption, we calculate: ⇒ Decrease in consumption = Q − Q ′ = Q − Q/ 1.12 = Q ( 1 − 1/ 1.12 )  Calculating 1 − 1 / 1.12 

⇒ 1 − 1/ 1.12 = 1 − 0.892857 = 0.107143

⇒ Now, converting this to a percentage: Percentage decrease = 0.107143 × 100 ≈ 10.71 %

Thus, the percentage decrease in petrol consumption required to maintain the same expenditure is approximately: 3) 10.7%.