\nLet the original price of petrol per unit be P and the original consumption be C units.
\nThe original expenditure on petrol = P * C.
\nThe petrol price hikes by 12%.
\nThe new price P’ = P + 12% of P = P + 0.12P = 1.12P.
\nLet the new consumption be C’.
\nThe new expenditure on petrol = P’ * C’ = 1.12P * C’.
\nThe condition is that there is no change in expenditure.
\nOriginal expenditure = New expenditure
\nP * C = 1.12P * C’.
\nDivide both sides by P (assuming P > 0):
\nC = 1.12 * C’.
\nC’ = $\\frac{C}{1.12}$.
\nThe decrease in consumption = Original Consumption – New Consumption = C – C’.
\nDecrease = $C – \\frac{C}{1.12} = C \\left(1 – \\frac{1}{1.12}\\right) = C \\left(\\frac{1.12 – 1}{1.12}\\right) = C \\left(\\frac{0.12}{1.12}\\right)$.
\nThe percentage decrease in consumption is $\\frac{\\text{Decrease in consumption}}{\\text{Original consumption}} \\times 100$.
\nPercentage decrease = $\\frac{C \\left(\\frac{0.12}{1.12}\\right)}{C} \\times 100 = \\frac{0.12}{1.12} \\times 100$.
\n$\\frac{0.12}{1.12} = \\frac{12}{112}$.
\nPercentage decrease = $\\frac{12}{112} \\times 100 = \\frac{3}{28} \\times 100 = \\frac{300}{28} = \\frac{75}{7}$.
\nNow calculate the value of $\\frac{75}{7}$ as a decimal:
\n$75 \\div 7 \\approx 10.714…$.
\nRounding to one decimal place, this is approximately 10.7%.
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