The price of sugar is increased by 20%. Manoj can increase his expenditure on sugar by only 15% from his income. In order to balance his expenditure, by what percentage should he reduce the quantity of sugar consumed?
4 1/6 %
Expenditure is the product of price and quantity, so \(E = P \times Q\).
Take the original price and quantity as 100 each, giving an original expenditure of \(100 \times 100 = 10000\).
The new price is 20% higher: \(120\). The allowed new expenditure is 15% higher: \(11500\).
So the new quantity is \(Q = \frac{11500}{120} = \frac{575}{6} = 95\frac{5}{6}\) units.
The reduction in quantity is \(100 - 95\frac{5}{6} = \frac{1}{6}\) of the original, that is \(4\frac{1}{6}\%\).
Hence, the answer is \(4\frac{1}{6}\%\).
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